A soccer ball is kicked on a field and follows the path of a parabola. It reaches a maximum height of 80 feet above the ground after traveling 160 feet from where it was kicited.a) Draw a diagram to represent this situation.b) Write an exact equation in vertex form to model this situation.c) Suppose there is a 30 feet tree 280 feet from where the ball was kicked. Will the ball sail over the tree? If yes, by how much? If not, by how much?
Answers
a) We will draw the situation.
b) Considering the theory, the vertex of a parabola is represented in (h,k) where h is the x-coordinate, in this case, if our parabola has an amplitude of x=320feet then h=320/2=160feet, and k is the highest y-coordinate 80 feet. So the equation is:
[tex]\begin{gathered} y=a(x-h)^2+k \\ y=a(x-160)^2+80 \end{gathered}[/tex]We have to know the value for a, so we will use a point to replace it in the equation and with that, we will know the value, so in x=0 the y-value is 0 too so:
[tex]\begin{gathered} 0=a(0-160)^2+80 \\ a(-160)^2=-80 \\ a=-\frac{80}{25600}=-\frac{1}{320} \end{gathered}[/tex]So the equation is:
[tex]y=-\frac{1}{320}(x-160)^2+80[/tex]c. To know the answer to this question we will have to replace x=280feet with the y value we will know if at the moment the ball can go over the tree or if it would crash into it.
[tex]\begin{gathered} y=-\frac{1}{320}(280-160)^2+80 \\ y=35feet \end{gathered}[/tex]At that point, the ball would be 35 feet up so if it could pass over the tree 5 feet higher.
Related Questions
I need this answered please
Answers
The rate of the slowest car is 86 km/hr using the concept of relative velocity.
What is Relative velocity?Relative speed is the rate at which one moving body moves in relation to another. The differential between two moving bodies determines their relative speed while they are traveling in the same direction. However, when two bodies are traveling in opposition to one another, the relative speed is determined by averaging their respective speed.
Let the speed of 1st car is v₁.
Let the speed of 2nd car is v₂.
v₁- v₂ = 18 km/hr --- (1)
And using the concept of relativity.
S(rel) = D(rel)/time
S(rel) = 360 / 2
S(rel) = 190
v₁ + v₂ = 190 --- (2)
Adding equations 1 and 2 we get
v₁ = 104 km/hr
v₂ = 86 km/hr
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Rewrite one eighth times x cubed times y plus seven eighths times x times y squared using a common factor.
Answers
Equation y (1/8 x3 + 7) is rewritten by using a common factor. A literal equation is regarded as having at least two variables.
Given that,
Use a common factor to rewrite one eighth times x cubed times y plus seven eighths times x times y squared.
This is how the equation can be rewritten:
The first equation is written as 1/8 x3y + 7/8 xy2.
It is possible to rewrite the equation 1/8 xy(x2 + y) using the common factor.
Equation two:
1/4x.y.4x2 + 28y
1/4 .4 x³ .y + 28y
x3.y + 28y equation to be solved
Using the formula
y = (x3 + 28).
Third claim:
1/4. x. y. x2 + 7y
Fix the problem.
1/4 . x³ .y + 7y
Write y = (1/4x3 + 7) in a new way.
Fourth assertion:
1/8 x3y2.y + 7 x 1/8 x3y3 + 7 x
After removing the common element x(1/8 x2y3+ 7), rewrite the equation.
Fifth Declaration
1/8 x. y. x² + 7y
1/8 x³. y + 7y
Equation y (1/8 x3 + 7) is rewritten.
Thus, a literal equation is one that contains at least two variables. Solve for one variable in terms of the other variable to rephrase a literal equation.
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A wholesaler sells a guitar for $1,396.20. What is the percent markup based on cost if the wholesaler paid $780 for the guitar?
Answers
The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%
Given,
The cost price of the guitar = $780
The selling price of the guitar = $1396.20
We have to find the markup percent based on the cost;
Markup percentage;
The gross profit of a unit, which is its sales price less its cost to produce or acquire for resale, is divided by the unit's cost to determine the markup %.
Markup percent = (Selling price - cost price) / cost price x 100
= (1396.20 - 780) / 780 x 100
= 616.20 / 780 x 100
= 0.79 x 100
= 79%
That is,
The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%
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Find the range, the standard deviation, and the variance for the given samples. Round non-integer results to the nearest tenth.−10, −16, −21, −24, −4, −30, −32 range ________standard deviation __________variance __________
Answers
From the given values, we can see that the lowest values is -32 and the highest value ie -4. Since the range is the difference betwwwn the highest and the lowest value, the range is
[tex]\begin{gathered} \text{Range}=-4-(-32) \\ \text{Range}=28 \end{gathered}[/tex]On the other hand, the sample variance formula is
[tex]S^2=\sqrt[]{\frac{\sum ^7_{n\mathop=1}(x-\bar{x})^2}{n-1}}[/tex]where x^bar is the mean and n is the total number of sample elements. In our case, n=7 and the mean is
[tex]\begin{gathered} \bar{x}=\frac{-10-16-21-24-4-30-32}{7} \\ \bar{x}=-\frac{137}{7} \\ \bar{x}=-19.5714 \end{gathered}[/tex]Then, the sample variance is given by
[tex]\begin{gathered} S^2=\frac{(-10-19.57)^2+(-16-19.57)^2+(-21-19.57)^2+\cdot\cdot\cdot+(-32-19.57)^2}{6} \\ S^2=105.2857 \end{gathered}[/tex]Since the standard deviation is the square root of the sample variance, we have
[tex]\begin{gathered} S=\sqrt[]{105.2857} \\ S=10.26088 \end{gathered}[/tex]By rounding the solutions to the nearest tenth, the answers are:
[tex]\begin{gathered} \text{Range}=28 \\ \text{Variance}=105.3 \\ \text{ Standard deviation = 10.3} \end{gathered}[/tex]A painter has three partially filled paint cans.1 7/8 gallonsthe second contains 1 1/5 gallonsand the third contains 1 3/4which anwer is closet to the total amount of paint?A.2B.3C.4D.5
Answers
A painter has three partially filled paint cans.
The first contains 1 7/8 gallons
The second contains 1 1/5 gallons
The third contains 1 3/4 gallons
The total amount of paint is the sum of these paint cans.
[tex]total=1\frac{7}{8}+1\frac{1}{5}+1\frac{3}{4}[/tex]Now let us add these mixed fraction numbers
[tex]\begin{gathered} total=1\frac{7}{8}+1\frac{1}{5}+1\frac{3}{4} \\ total=(1+1+1)+(\frac{7}{8}+\frac{1}{5}+\frac{3}{4}) \\ total=(3)+(\frac{7}{8}+\frac{1}{5}+\frac{3}{4}) \\ total=(3)+(1.825) \\ total=4.825 \end{gathered}[/tex]As you can see, 4.825 is closest to 5.
Therefore, the correct option would be D
Find the x- and y-intercepts of the graph of 4x-4y=324x−4y=32. State each answer as an integer or an improper fraction in simplest form.
Answers
Answer:x-intercepts (5,0)
y-intercepts (0,-5)
Step-by-step explanation: To find the x-intercept substitute in 0 for y and solve for x. to find the y-intercept subsitute 0 for x and solve for y
Find the value of x .
Answers
Answer:
x = 113
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 8 , then
sum = 180° × 6 = 1080°
sum the interior angles and equate to 1080
x + 137 + 144 + 139 + 123 + 150 + 142 + 132 = 1080
x + 967 = 1080 ( subtract 967 from both sides )
x = 113
A poster is
than
25 cm taller
it is wide. It is
mounted on a piece
of cardboard so
that there is a 5
cm border on all
sides.
If the
area of the border
alone is 1350 cm²,
what are the
dimensions of the
poster
Answers
The dimension are 75 * 50 i.e, Width = 50 cm , Length = 75 cm
Define Dimension
A measurable extent of a particular kind, such as length, breadth, depth, or height.
Let,
T = how taller the poster is
W = how wide the poster is
According to question given,
T = W + 25 ---eq(i)
The total height is calculated by multiplying the top border by 5 and the bottom border by 5. The entire height is then multiplied by the border's width, 5, times 2, so there are two tall sides. then multiplying by 5 times 2 widths.The equation looks like that,
5 * (2 (T + 10)) + 5 * (2 * W) = 1350
Now substitute the eq(i) value,
5 * (2 ((W + 25) + 10)) + 5 * (2 * W) = 1350
Now, solve for W,
5 * (2W +50 + 20) + 10W = 1350
10W + 5(70)+ 10W = 1350
20W + 350 = 1350
20W = 1350 - 350
20W = 1000
W = 1000/20
W = 50
Now, put the W value in eq(i)
T = 50 + 25
T = 75
Therefore, The dimension are 75 * 50 i.e, Width = 50 cm , Length = 75 cm
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In triangle ABC measure of angle A equals 45°. The altitude divides the side AB into two parts of 20 and 21 units. Find BC.
Answers
In triangle ABC, BC = 29 units.
Given,
In Δ ABC, ∠A = 45°.
A perpendicular line segment traced from a triangle's vertex to its opposite side is said to be the triangle's altitude.
Let altitude meet AB on D.
So, AD = 20 units and DB = 21 units and ∠ADC = ∠BDC = 90°
In ΔADC,
tan A = DC/AD
tan 45° = DC/20
1 = DC/20
DC = 20 units
In ΔBDC,
BC² = BD² + DC² (Pythagorean Theorem)
= 21² + 20²
= 441 + 400
= 841
BC = √841
= 29
Hence, BC = 29 units.
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#5 Pam a nurse made $93 in 6 hours determine an equation that represents how much she gets paid per hour #6 using your equation from problem 5 how much would a modern if she work for 15 hours?#7 using your equation from problem 6 how much would Pam earn if she work for 3 1/2 hours?
Answers
Pam is a nurse that earns $93 in 6 hrs .The equation that can represents how much she get paid per hour can be computed below
[tex]\begin{gathered} \text{ amount she earned per hr=}\frac{93}{6}=15.5 \\ The\text{ equation that can represent how much she earned per hour is} \\ \text{amount earned per hour = 15.5x} \\ x=\text{ hours worked} \\ \text{amount earned per hour}=15.5(1)=15.5\text{ dollars} \end{gathered}[/tex][tex]\begin{gathered} \text{amount she earned in 15 hrs=}15.5x \\ \text{amount she earned in 15 hrs}=15.5\times15=232.5dollars \end{gathered}[/tex][tex]\begin{gathered} \text{amount earned in 3}\frac{1}{2}\text{hrs}=15.5x \\ \text{amount earned in 3}\frac{1}{2}\text{hrs=15.5}\times\frac{7}{2}=\frac{108.5}{2}=54.25dollars \end{gathered}[/tex]Please Help :))
Given:
Prove: AABC = ACDA.
Step
-
2
try
Statement
ZB ZD
BC AD
AC
AC
Type of Statement
B
Reason
Given
Reflexive Property
D
Answers
3) [tex]\angle BCA \cong \angle CAD[/tex] (alternate interior angles theorem)
4) [tex]\triangle ABC \cong \triangle CDA[/tex] (AAS)
help please!! Which of the following functions is graphed below? brainly and 100
Answers
The absolute value function graphed in this problem is given as follows:
A. y = |x - 5| - 4.
How to define the absolute value function?An absolute value function of vertex (h,k) is defined as follows:
y = a|x - h| + k.
The leading coefficient a does not influence the vertex of the absolute value function.
The vertex of the graph is the turning point, hence it is given as follows:
(5, -4).
Hence, considering a leading coefficient 1, h = 5 and k = -4, the equation is given as follows:
y = |x - 5| - 4.
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2The shape shown is made up of three similar right-angled triangles.22The smallest triangle has two sides of side-length 2, as shown.What is the area of the shape?1412 + 12V22824 + 20V56Erase
Answers
The triangles are similar. The smaller is isosceles, so the 3 of them are as well.
Let's Start by finding the hypotenuse of the smaller one:
a² = 2
Simplify using order of operation 10^2-2[12-(3-2)]
Answers
Given the expression:
[tex]10^2-2\lbrack12-(3-2)\rbrack[/tex]We start from the parenthesis inside the brackets. We know that 3-2=1, then:
[tex]10^2-2\lbrack12-(3-2)\rbrack=10^2-2\lbrack12-(1)\rbrack=10^2-2\lbrack11\rbrack[/tex]now, we have that 10^2=100 and 2*11 =22, then:
[tex]10^2-2\lbrack11\rbrack=100-22=78[/tex]therefore, the result of simplifying the expression is 78
Got another one for yall
Answers
The height, h of the parallelogram is 4 feet.
How to find the height of a parallelogram?A parallelogram is a quadrilateral with opposites sides equal to each other. Opposite sides of a parallelogram are also parallel to each other.
Opposite angles of a parallelogram are congruent. The consecutive or adjacent angles of a parallelogram is supplementary.
Therefore, the height of the parallelogram can be found as follows:
The sum of angles in a parallelogram is 360 degrees.
Hence,
sin ∅ = opposite / hypotenuse
where
∅ = one angle of the parallelogramsin ∅ = 3 / 6
sin ∅ = 1 / 2
∅ = sin⁻¹ 0.5
∅ = 30
Therefore,
30 + 30 + 2x = 360
where
x = angle of the parallelogram60 + 2x = 360
2x = 360 - 60
2x = 300
x = 300 / 2
x = 150
Let's find the height of the parallelogram using trigonometric ratios,
sin 30° = h / 8
cross multiply
h = 8 sin 30°
h = 8 × 0.5
Therefore,
h = 4 ft
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the admission fee at an amusement park is $2.00 for children and $7.00 for adults. on a certain day, 299 people entered the park, and the admission fees collected totaled $1573. how many children and how many adults were admitted?
Answers
Answer:
104 children and 195 adults
Step-by-step explanation:
let a represent number of adults and c represent number of children , then
a + c = 299 → (1)
7a + 2c = 1573 → (2)
multiplying (1) by - 2 and adding to (2) will eliminate c
- 2a - 2c = - 598 → (3)
add (2) and (3) term by term to eliminate c
5a + 0 = 975
5a = 975 ( divide both sides by 5 )
a = 195
substitute a = 195 into (1) and solve for c
195 + c = 299 ( subtract 195 from both sides )
c = 104
104 children and 195 adults were admitted
A rectangular prism is 9 inches long, 3 inches wide, and _____ inches high.
The volume of the box is 324 in.
What is the height of the box?
Answers
Answer:
height = 12
Step-by-step explanation:
try and use the formula to plug it in and solve for x.
solve the equation, giving values of x in a form suitable for computation.
x(2√3-3)=4√3
answer = 8+4√3
(never heard of computation before
Answers
Answer:
x = 8 + 4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
computation just means to calculate
x(2[tex]\sqrt{3}[/tex] - 3 ) = 4[tex]\sqrt{3}[/tex] ( divide both sides by (2[tex]\sqrt{3}[/tex] - 3 ) )
x = [tex]\frac{4\sqrt{3} }{2\sqrt{3-3} }[/tex]
rationalise the denominator by multiplying the numerator/ denominator by the conjugate of the denominator.
the conjugate of 2[tex]\sqrt{3}[/tex] - 3 , is 2[tex]\sqrt{3}[/tex] + 3
= [tex]\frac{4\sqrt{3}(2\sqrt{3}+3) }{(2\sqrt{3}-3)(2\sqrt{3}+3) }[/tex] ← expand denominator using FOIL
= [tex]\frac{24+12\sqrt{3} }{12-9}[/tex]
= [tex]\frac{24+12\sqrt{3} }{3}[/tex]
= [tex]\frac{24}{3}[/tex] + [tex]\frac{12\sqrt{3} }{3}[/tex]
= 8 + 4[tex]\sqrt{3}[/tex]
What is the slope of y = -5x - 11
Answers
Answer:
0
Step-by-step explanation:
Select all the intervals where f is decreasing.(Choice A)-5
Answers
Looking at the graph
we have that
Decreasing intervals are
(-infinite, -2.5) and (1.75, infinite)
so
Verify each option
A ----> is true
B ---> is not true
C ---> is true
D ---> is not true
The answer is A and CHELP ME PLEASE I NEED HELP I DONT KNOW HOW TO DO THIS
Answers
Answer:
convert miles to kilometers by multiply by 1.61 covert kilometers to miles by devide by 0.62(if am not wrong)
Please help me I only have 3 minutes left to do this
Answers
486lb of grass seed is required to cover the field on the right.
What is Area of Rectangle?The area of Rectangle is length times of width
Let us find the areas of two rectangle larger and smaller.
Area of the larger rectangle:
60×90=5400 square feet.
Now divide the larger square area by the smaller square area:
Area of the smaller rectangle
40×50=200 square feet.
Now divide larger rectangle with smaller
5400/200 =27
27 is the ratio of the difference
27×18=486 lb.
Hence 486lb of grass seed is required to cover the field on the right.
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a recipe calls for 40 ounces of rice. how many grams of rice dose the recipe require
Answers
Answer:
1133.98
almost 1134 grams :)
Step-by-step explanation:
multiply by 28.35 to get the answer :)
Answer:
1133.98
Step-by-step explanation:
Hope it helps and have a nice day!!!!! :)
BRAINIEST IS APPRECIATED!!!
This question has two parts. First, answer Part A. Then, answer Part B.
part A:
Answers
The length of the incline of the ramp will be [h] = 12.0415 ft
What is Pythagoras theorem?According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the base and perpendicular. Mathematically, we can write -
h² = p² + b²
Given is the installation of wheelchair ramp such that the ramp should have a base of 12 ft and height of 1 ft long.
From the data given, we can consider the ramp construction as right angled triangle. We can write -
base [b] = 12 ft
height [p] = 1 ft
Using the Pythagoras theorem -
h² = (12 x 12) + (1 x 1)
h² = 144 + 1
h = √145
h = 12.0415
Therefore, the length of the incline of the ramp will be [h] = 12.0415 ft
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[This question also has part B. Visit the following link for part B -
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Is the function positive or negative over the interval (–8, –6)?
Answers
Answer:negative
Step-by-step explanation:
Because it should be on the bottom left corner if you are using a graph it is different in each corners of the graph. There is four sides for the graph.
SHOW YOUR WORK
2 x 1/4 =
Answers
Answer:
2 times 1/4 = 1/2 or 0.5
Step-by-step explanation:
Step 1: Setup
First of all, note that 2 is the same as 2/1 since 2 divided by 1 is 2. Therefore, start by setting up the problem like this:
2/1 x 1/4
Step 2: Multiply
Multiply the numerators together (2 x 1 = 2) and multiply the denominators together (1 x 4 = 4) and make it into one fraction like so:
2/4
Step 3: Minimize
The greatest common factor of 2 and 4 is 2. Minimize the fraction by dividing the numerator and the denominator by its greatest common factor to get the answer as follows:
1/2
HELP PLEASE!!!!! i'M GIVING 30 POINTS
Answers
The intensity of the dishwasher will be 44.44 times the maximum intensity.
What is intensity of sound?
Sound intensity, also known as acoustic intensity, is defined as the power carried by sound waves per unit area in a direction perpendicular to that area. Mathematically, we can write the intensity of sound as -
[tex]\mathrm {I} =2\pi ^{2}\nu ^{2}\delta ^{2}\rho c[/tex]
Given is the sound intensity as measured in decibels and its measurement for a dishwasher is 37 decibels.
The given formula is -
db = 10 log(I/I₀)
Substituting the values, we get -
37 = 10 log(I/I₀)
log(I/I₀) = (37/10)
log(I/I₀) = (37/10)
(I/I₀) = e ^ (37/10)
I/I₀ = 40.44
I = 40.44I₀
Therefore, the intensity of the dishwasher will be 44.44 times the maximum intensity.
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A triangle has side lengths of 10 inches, 11 inches, and 12 inches. What kind of triangle is it?
Answers
Answer:
Acute scalene triangle.
More Information:
Sides: a = 10 b = 11 c = 12
Area: T = 51.521
Perimeter: p = 33
Semiperimeter: s = 16.5
Angle ∠ A = α = 51.318° = 51°19'4″ = 0.896 rad
Angle ∠ B = β = 59.17° = 59°10'10″ = 1.033 rad
Angle ∠ C = γ = 69.513° = 69°30'46″ = 1.213 rad
Height: ha = 10.304
Height: hb = 9.367
Height: hc = 8.587
Median: ma = 10.368
Median: mb = 9.579
Median: mc = 8.631
Inradius: r = 3.122
Circumradius: R = 6.405
Vertex coordinates: A[12; 0] B[0; 0] C[5.125; 8.587]
Centroid: CG[5.708; 2.862]
Coordinates of the circumscribed circle: U[6; 2.242]
Coordinates of the inscribed circle: I[5.5; 3.122]
Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 128.682° = 128°40'56″ = 0.896 rad
∠ B' = β' = 120.83° = 120°49'50″ = 1.033 rad
∠ C' = γ' = 110.487° = 110°29'14″ = 1.213 rad
How to Solve:
The calculation of the triangle has two phases. The first phase calculates all three sides of the triangle from the input parameters. The first phase is different for the different triangles query entered. The second phase calculates other triangle characteristics, such as angles, area, perimeter, heights, the center of gravity, circle radii, etc. Some input data also results in two to three correct triangle solutions (e.g., if the specified triangle area and two sides - typically resulting in both acute and obtuse) triangle).
1. Input data entered: sides a, b, and c.
a=10
b=11
c=12
We know the lengths of all three sides of the triangle, so the triangle is uniquely specified. Next, we calculate another of its characteristics - the same procedure for calculating the triangle from the known three sides SSS.
a=10
b=11
c=12
2. The triangle perimeter is the sum of the lengths of its three sides
3. Semiperimeter of the triangle
The semiperimeter of the triangle is half its perimeter. The semiperimeter frequently appears in formulas for triangles to be given a separate name. By the triangle inequality, the longest side length of a triangle is less than the semiperimeter.
4. The triangle area using Heron's formula
Heron's formula gives the area of a triangle when the length of all three sides is known. There is no need to calculate angles or other distances in the triangle first. Heron's formula works equally well in all cases and types of triangles.
5. Calculate the heights of the triangle from its area.
There are many ways to find the height of the triangle. The easiest way is from the area and base length. The triangle area is half of the product of the base's length and height. Every side of the triangle can be a base; there are three bases and three heights (altitudes). Triangle height is the perpendicular line segment from a vertex to a line containing the base.
6. Calculation of the inner angles of the triangle using a Law of Cosines
The Law of Cosines is useful for finding a triangle's angles when we know all three sides. The cosine rule, also known as the Law of Cosines, relates all three sides of a triangle with an angle of a triangle. The Law of Cosines extrapolates the Pythagorean theorem for any triangle. Pythagorean theorem works only in a right triangle. Pythagorean theorem is a special case of the Law of Cosines and can be derived from it because the cosine of 90° is 0. It is best to find the angle opposite the longest side first. With the Law of Cosines, there is also no problem with obtuse angles as with the Law of Sines because the cosine function is negative for obtuse angles, zero for right, and positive for acute angles. We also use inverse cosine called arccosine to determine the angle from the cosine value.
7. Inradius
An incircle of a triangle is a tangent circle to each side. An incircle center is called an incenter and has a radius named inradius. All triangles have an incenter, and it always lies inside the triangle. The incenter is the intersection of the three-angle bisectors. The product of the inradius and semiperimeter (half the perimeter) of a triangle is its area.
8. Circumradius
The circumcircle of a triangle is a circle that passes through all of the triangle's vertices, and the circumradius of a triangle is the radius of the triangle's circumcircle. The circumcenter (center of the circumcircle) is the point where the perpendicular bisectors of a triangle intersect.
9. Calculation of medians
A median of a triangle is a line segment joining a vertex to the opposite side's midpoint. Every triangle has three medians, and they all intersect each other at the triangle's centroid. The centroid divides each median into parts in the ratio of 2:1, with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex. We use Apollonius's theorem to calculate the length of a median from the lengths of its side.
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Translate and solve: negative eighty times r is less than 80
Answers
r > -1
Explanations:Negative eighty times r is less than 80 is expressed mathematically as;
[tex]-80r<80[/tex]Divide both sides by -80.
[tex]\begin{gathered} \frac{-80r}{-80}<-\frac{80}{80} \\ r>-1 \end{gathered}[/tex]Note the change in sign when divided by a negative value
The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. On a certain day, 335 people entered the park, and the admission fees collected totaled 940 dollars. How many children and how many adults were admitted?
Answers
Let
number of children admitted = x
number of adult admitted = y
Total number admitted = 335
[tex]\begin{gathered} x+y=335 \\ 1.5x+4y=940 \\ x=335-y \\ 1.5(335-y)+4y=940 \\ 502.5-1.5y+4y=940 \\ 502.5+2.5y=940 \\ 2.5y=940-502.5 \\ 2.5y=437.5 \\ y=\frac{437.5}{2.5} \\ y=175 \\ x+y=335 \\ x+175=335 \\ x=335-175 \\ x=160 \end{gathered}[/tex]number of children = 160
number of adult = 175
