Two hundred eighty-two people attended a recent performance of Cinderella. Adult tickets sold for $5 and children’s tickets sold for $3 each. Find the number of adults and the number of children that attended the play if the total revenue was $1046.
Part A: Write a system of equations in standard form (Ax + By = C) that can be solved to find the number of adults and children who attended the performance. Define the variables used in the equations. (4 points)
Part B: How many adults attended the performance? How many children attended the performance? Show your work and steps of how you found your answer using elimination.
Answers
A. A system of equations in standard form that can be solved to find the number of adults and children who attended the performance is:
x + y = 282
3x + 5y = 1046
B. The number of adults who attended the performance is 182 adults.
The number of children who attended the performance is 100 children.
How to determine the number of each type of tickets sold?In order to write a system of linear equations to describe this situation, we would assign variables to the number of adult tickets sold and number of children tickets sold, and then translate the word problem into an algebraic equation as follows:
Let the variable x represent the number of adult tickets sold.Let the variable y represent the number of children tickets sold.Since 282 people attended the recent performance by Cinderella, a linear equation that models the situation is given by:
x + y = 282 ....equation 1.
Additionally, adult tickets sold for $5 while children tickets sold for $3 each with a total revenue was $1046, a linear equation that models the situation is given by:
3x + 5y = 1046 .......equation 2.
Part B.
By multiplying equation 1 by 3, we have:
3x + 3y = 846 .......equation 3.
By subtracting equation 3 from equation 2, we have:
2y = 200
y = 100 children.
For the x-value, we have:
x = 282 - y
x = 282 - 100
x = 182 adults.
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Related Questions
The temperature in a hotel is 21 °C.
The temperature in the hotel is 26,7°C warmer than at the top of the mountain.
The temperature at the top of the mountain is 3.2°C colder than at the bottom of the mountain.
Work out the temperature at the bottom of the mountain.
Answers
The temperature at the bottom of the mountain is 50.9 °C.
Let's work through the given information step by step to find the temperature at the bottom of the mountain.
The temperature in the hotel is 21 °C.
The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.
Let's denote the temperature at the top of the mountain as T_top.
So, the temperature in the hotel can be expressed as T_top + 26.7 °C.
The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.
Let's denote the temperature at the bottom of the mountain as T_bottom.
So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.
Now, let's combine the information we have:
T_top + 26.7 °C = T_bottom - 3.2 °C
To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:
T_bottom = T_top + 26.7 °C + 3.2 °C
T_bottom = T_top + 29.9 °C
Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:
T_bottom = 21 °C + 29.9 °C
T_bottom = 50.9 °C
Therefore, the temperature at the bottom of the mountain is 50.9 °C.
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Destiny owns a cake shop and she is working on two wedding cakes this week. The first cake consists of 4 small tiers and 4 large tiers, which will serve a total of 288 guests. The second one includes 3 small tiers and 5 large tiers, which is enough servings for 316 guests. How many guests does each size of tier serve?
A small tier will serve guests and a large tier will serve guests.
Answers
Answer:
small tier: 22large tier: 50Step-by-step explanation:
If cakes of 4 small and 4 large tiers serve 288 guests, and 3 small and 5 large tiers serve 316 guests, you want to know the number of guests served by a tier of each size.
SetupLet 's' and 'l' represent the numbers of guests served by small and large cake tiers, respectively. The first cake serves ...
4s +4l = 288
And the second cake serves ...
3s +5l = 316
SolutionSubtracting 3/4 of the first equation from the second gives ...
(3x +5l) -3/4(4s +4l) = (316) -3/4(288)
2l = 100
l = 50
4s +4(50) = 288 . . . substitute for l in the first equation
4s = 88 . . . . . . . . . . subtract 200
s = 22 . . . . . . . divide by 4
A small tier will serve 22 guests; a large tier will serve 50 guests.
HELP PLSSSS I need help BEFORE MY MOM WHIp MEEE
Answers
Answer:
the answer is 8
Step-by-step explanation:
;)
Need help with question
Answers
Answer:
f(2) = 1
x = 0
Step-by-step explanation:
f(2) = 1 since y=1 when x=2.
f(0) = -3 since x=0 when y=-3
Solve y = ax² + c for x.
O x
x= ± √ay-c
O
O
x = ±₁
X=
X=
у-с
a
y
y + c
a
Answers
In the quadratic equation y = a\(x^{2}\) + c ,the value of x = ± \(\sqrt \frac{y-c}{a}\)
A quadratic equation is any equation containing one term wherein the unknown is squared and no term wherein it's far raised to a higher power.
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, in which a and b are the coefficients, x is the variable, and c is the constant term.
To find the value of x
Assuming \(a\neq o\)
First, subtract c from both the sides to get:
\(y-c=ax^{2}\)
then, divide both sides by \(a\) and transpose to get:
\(x^{2} =\frac{y-c}{a}\)
So, \(x\) must be a square root of \(\frac{y-c}{a}\) and we can deduce:
\(x=\) ± \(\sqrt \frac{y-c}{a}\)
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Rewrite the function f(x)=2(x-2)^2+6 in the form f(x)=ax^2+bx+c.
Answers
Answer:
To write a polynomial in standard form, simplify and then arrange the terms in descending order.
f(x)=ax²+bx+c
Simplify each term.
f(x)=2x²−8x+8+6
Add 8 and 6.
f(x)=2x²−8x+14
Step-by-step explanation:
Select the correct answer. Consider matrices A, B, and C:
Answers
Answer:
i think it is c. i may be incorrect, i am sorry!
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
I did the math
Convert each rate using dimensional analysis 44yds/s=?mi/h
Answers
Using dimensional analysis we have converted 44 yards/sec = 90 miles/hour.
What is dimensional analysis?Dimensional analysis is the study of how dimensions and units of measurement affect the relationship between physical quantities.
Dimensional analysis is crucial because it maintains the consistency of the units, which facilitates accurate mathematical computation.
As we use conversion factors to obtain the same units, dimensional analysis is also known as the Factor Label Method or Unit Factor Method.
We know that 1 yards/sec = 2.04545 miles/hour
Here given that 44yds/s = ? miles/hour
Lets solve
1 yards/sec = 2.04545 miles/hour
44 yards/sec = 44 × 2.04545 miles/hour
44 yards/sec = 89.9998 miles/hour
44 yards/sec = 90 miles/hour
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What is the probability that you will be able to draw all of the cards in the deck without being forced to stop because you have $0 in your pocket?
Answers
Step-by-step explanation:
Probability will be 0 According to me!!
Mark me BRAINLIESTMrs. Grubbs has the option of eating a cookie with the diameter of 14 cm or 4 smaller cookies with a diameter of 5
cm. Which option would give Mrs. Grubbs more cookie to eat?
Answers
Mrs. Grubbs would get more cookie to eat by choosing the 4 smaller cookies with diameter 5 cm each rather than the single cookie with diameter 14 cm.
To compare the amount of cookie Mrs. Grubbs would get by eating a single cookie with diameter 14 cm and 4 smaller cookies with diameter 5 cm each, we need to consider the total area of the cookies.
The area of a cookie with diameter 14 cm can be calculated as follows:
A = πr^2 = π(7 cm)^2 = 49π cm^2
where r is the radius of the cookie.
On the other hand, the area of a single small cookie can be calculated as follows:
A1 = \(πr^2\) = \(π(2.5 cm)^2\)= \(6.25π cm^2\)
where r is the radius of the small cookie.
Therefore, the total area of 4 small cookies is:
A2 = 4A1 = \(4(6.25π cm^2)\) = \(25π cm^2\)
Comparing the two options, we see that the total area of the 4 small cookies is greater than the area of the single large cookie:
A2 > A
\(25π cm^2 > 49π cm^2\)
It's worth noting that this comparison assumes that the thickness or volume of the cookies is the same for both options. If the cookies have different thicknesses, then the comparison would need to take into account the volume of the cookies instead of just the area.
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Help pls George is building a fence around a rectangular dog run. He is using his house as one side of the run. The area of the dog run will be 240 square feet. The length of the run is 30 feet, and the width is (30 minus x) feet. The diagram below shows his plan.
Recall the formulas for area and perimeter: A = lw and P = 2l + 2w.
Answers
The width of the dog run is 20 feet.
In the given problem, the length of the dog run is given as 30 feet.
The area of the dog run is also given as 240 square feet.
Using the formula for the area of a rectangle (A = lw), we can solve for the width (w).
Rearranging the formula, we have w = A / l.
Plugging in the values, we get w = 240 / 30 = 8 feet.
Since the width is given as (30 minus x) feet, we can set up an equation:
30 - x = 8. Solving for x, we find x = 22.
Therefore, the width of the dog run is 20 feet (30 - 22 = 8).
In this problem, the length and width of the dog run are defined by the dimensions of the fence being built around it.
The area of the dog run is given as 240 square feet.
By using the formula for the area of a rectangle, we can solve for the width. We are also given that the length is 30 feet.
Setting up an equation with the given width (30 minus x) and solving for x, we find that x is equal to 22.
This means that the width of the dog run is 8 feet. The main answer to the problem is that the width of the dog run is 20 feet (30 - 22 = 8).
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What is the answer to the following?
1. 8/9 divide by 2/3
2. 4 divided by 3/4
3. 2 1/2 divided by 3/4
4. 4/9 divided by 5 1/3
5. 7/8 divided by 14
Answers
i would go with either a or b
What is the solution of the system of
equations shown in the graph?
(1.5, -3)
(-3, 1.5)
X
(-3,0)
(0, -3)
Answers
Answer: (-3, 0)
--------------------
desmos
Unit 6.2, Lesson 10: Practice Problems
Inola is making personal pizzas for her birthday party. For 4 pizzas, she uses 10 ounces of cheese.
At this rate, how much cheese does she need if she makes:
3.1 12 pizzas?
3.2
22 pizzas?
10
3.3 11 pizzas?
Answers
ANSWER:
3.1) 30 ounces
3.2) 55 ounces
3.3) 27.5 ounces
STEP BY STEP:
1. Find out how much cheese you need for one pizza.
10 divide 4 = 2.5
2. Multiply
3.1) 2.5 x 12 = 30
3.2) 2.5 x 22 = 55
3.3) 2.5 x 11 = 27.5
Astronomers measure large distances in light-years. One light-year is the distance that light can travel in one year, or approximately 5,880,000,000,000 miles. Suppose a star is 13.6 light-years from Earth. In scientific notation, how many miles away is it?
a)5.88 × 1012 miles
b)7.9968 × 1013 miles
c)5.88 × 1013 miles
d)1.36 × 1012 miles
Answers
Answer:
b) 7.9968 × 1013 miles
Step-by-step explanation:
So one light-year equals 588 × 10^10
13.6 light-years equals 13.6 × 588 × 10^10 = 79968 × 10^9 = 7.9968 × 1013 miles
The polynomial function for this graph is of (odd,even, abnormal)
degree and the leading coefficient is (positive,negative,zero)
Answers
Answer:
first graph: The polynomial function for this graph is of ✔ odd degree and the leading coefficient is ✔ negative.
second graph: The polynomial function for this graph is of ✔ even degree and the leading coefficient is ✔ negative.
Step-by-step explanation:
hope this helped
When the output value of a real-valued function, f(x), is equal to f(-x), for all values of x inside the domain of f, the function is said to be an even function.
It is claimed that a real-valued function f(x) is an odd function when, for all values of x in the domain of f, the output value of f(-x) is equal to the negative of f(x).
Given:
As, we know the first graph graph of an odd function is at the same distance from the origin but in opposite directions and, graph of an even function remains the same after reflection about the y-axis.
So, The polynomial function for this graph is of odd degree and the leading coefficient is negative.
and, The polynomial function for this graph is of even degree and the leading coefficient is negative.
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if 10 kilograms are 22 pounds how much is 5 1/2 in kilograms?
Answers
Answer:
for 1 pound =10/22
for 51/ 2 pounds = 10/22x51/2
= 510/ 44
= 11.590kg
Step-by-step explanation:
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Answers
A proportion is an equation that sets two ratios at the same value.For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)There are 1 in 4 boys and 3 in 4 girls.0.25 are male (by dividing 1 by 4)
Solve the problem ?The error committed by Josiah is (b) He failed to multiply the numerator and denominator by the appropriate amount to equal 1,500.
The ratio is stated as follows:
10/20 = X/1500
Add 1500 to both sides.
10/20 *1500
Interpret the expression on the right.
10/20*1500 = x
on the left, multiply by 1500 the number 10.
1500/20 =x
20 times 15000 divided left to right
750 = x
the equation as follows:
x = 750
We can tell that the products are poorly executed from the query.
Consequently, Josiah's error is (b)
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HELP!!
Next, you will make a scatterplot. Name a point that will be on your scatter plot and describe what it represents.
Answers
A point on the scatter plot is defined as (19, 3), which means that an input of 19 is mapped to an output of 3.
What is the scatter plot?The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:
(Input, Output).
One point on the scatter plot for this problem has the coordinates given as follows:
(19, 3).
Hence the meaning is that an input of 19 is mapped to an output of 3.
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1/3 2/7 Common
Denominator: ________
Answers
Answer:
21
Step-by-step explanation:
btw is it LDC or GCD?
Are these two expressions equivalent?
6 + 3 and 3 + 6
Answers
Answer: Yes its equivalent
Step-by-step explanation:
6 + 3 =9 and 3 + 6= 9
9 = 9
You should know this smh
USE THE Z-TABLE TO FIND THE AREA TO THE LEFT OF Z=2.09
Answers
Finding the left-side area in the z-distribution is basically finding the following probability:
\(\begin{gathered} P\text{ \lparen z < }\alpha)\text{ = left area} \\ 1-P(\text{z < }\alpha)\text{ = right area} \end{gathered}\)Consider alpha the value of z given by the exercise.
According to excel, this probability is equal to 0.982.
Another approach could be:
Solve for p.
4p + 2 ≤ 10
Answers
Answer:
p=2
Step-by-step explanation:
4p+2≤10
-2 -2
4p≤8
divide by 4
p≤2
Answer:
p ≤ 2
Step-by-step explanation:
FILL IN THE BLANK eigenvalues and eigenvectors of a matrix (optional) 0 points possible (ungraded) let , ____ and ____, where unanswered_____- , where unanswered . therefore, is an eigenvector of with eigenvalue , and is an eigenvector of with eigenvalue .
Answers
Let A be a matrix, v and λ be vectors. Therefore, Av = λv, where v is an eigenvector of A with eigenvalue λ, and if there is another non-zero vector w such that Aw = μw, then w is an eigenvector of A with eigenvalue μ. Therefore, v is an eigenvector of A with eigenvalue λ, and w is an eigenvector of A with eigenvalue μ.
Allow a to be a matrix, and v and λ to be vectors. Consequently, av = λv, wherein v is a non-zero vector and λ is a scalar. This means that v is an eigenvector of a with eigenvalue λ.
Further, if there may be every other non-0 vector w such that aw = μw, then w is an eigenvector of a with eigenvalue μ. The eigenvectors and eigenvalues of a matrix are vital in lots of packages, including fixing systems of linear equations, studying dynamical systems, and studying facts using strategies along with main thing evaluation.
By computing the eigenvectors and eigenvalues of a matrix, we will benefit perception of its shape and conduct, and use these records to solve problems and make predictions.
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Fill in this blank spaces (1,3,5,7,9 , 11, 13, 15) _+_+_=30
Answers
Step-by-step explanation:
Just till the number 9 upside down to make it 6 then
6+11+13=30
The sum of three odd numbers can never be even. so I did it in that way.
I HOPE THIS WILL HELP U
STAY SAFE, STAY HAPPY
please help me please i really need help please
Answers
Answer:
Step-by-step explanation:
V = 3.14 × r² × h
r= 20/2 =10 cm
h = 11 cm
V = 3.14 x10² x 11 = 3454 cm³
A library has 41 362 fiction books. It has 4825 non-fiction books fewer than fiction books. How many books does the library have in all?
Answers
Answer:
There are 77,899 books in the library
Step-by-step explanation:
1 step
41,362 - 4825 =36,537
2 step
41,362 + 36537 = 77,899
find the quotient 19 008 ÷ 16
Answers
Answer:1188
Step-by-step explanation:
What would be the slope of the positions (3,3) and (4,5)
Answers
Answer:
m = 2
Step-by-step explanation:
Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)
Simply plug our coordinates into the slope formula and solve for m:
m = (5 - 3)/(4 - 3)
m = 2/1
m = 2
Answer:
2Step-by-step explanation:
Let the points be A and B
A( 3 , 3 ) -----> ( x1 , y1 )
B(4 , 5 ) ------>( x2 , y2 )
Now,
finding the slope,
Slope =\( \frac{y2 - y1}{x2 - x1} \)
\( = \frac{5 - 3}{4 - 3} \)
\( = \frac{2}{1} \)
\( = 2\)
Hope this helps...
Good luck on your assignment..
Which of the following could be a real-world description of 5x − 18? (I ALSO NEED THIS FAST)
A: $18 in addition to the cost of 5 hot dog combos
B: The cost of 18 people splitting 5 hot dog combos
C: The cost of hot dog combos less an $18 coupon split by 5 people
D: $18 less than the cost of 5 hot dog combos
Answers
The correct answer is (C) The cost of hot dog combos less than an $18 coupon split by 5 people.