Write a system of equations to describe the situation below, solve using elimination, and fill in
the blanks.
The manager at a community pool is looking over receipts. On a certain Monday, the pool had
16 children and 42 adults, which brought in $142. That same week on Tuesday, 24 children
and 26 adults came to the pool, which brought in $102. What are the admission prices for
children and adults?

Answers

Answer 1

Answer:  Child is $1 and Adult is $3, per person.

Step-by-step explanation:

We have two unknowns, so we need at least two equations.  Let C and A stand for the price of a ticket for a child and an adult, respectively.

The income for Monday and Tuesday can be calculated:

Monday:   16C + 42A = $142

Tuesday:  24C + 26A = $102

Rearrange the second equation to isolate one of the variables.  I'll pick C:

24C + 26A = $102

C  = ($102 - 26A)/24

Now use this expression for C in the first equation

16C + 42A = $142

16(($102 - 26A)/24) + 42A = $142

16(($102 - 26A)/24) + 42A = $142

(1632 - 416A)/24 + 42A = $142

(68 - 17.3333A + 42A = $142

24.6667A = 74

A = 3  [The price of an adult pool admission is $3]

Use this value in either equation to find the price of a child's admission:

24C + 26A = $102

24C + 26*($3) = $102

24C = 102 - 78

C = $1   [The price of a child's admission to the pool is $1]

Check to see if these prices satisfy both equations:

Monday:   16C + 42A = $142

Tuesday:  24C + 26A = $102

---

Monday:   16*(1) + 42*(3)  = $142   ?   YES

Tuesday:  24*(1) + 26*(3) = $102   ?    YES

Child is $1 and Adult is $3, per person.


Related Questions

Please help asap! I will mark brainliest for correct answer!!
a softball player hits a pitched ball when it is 4 feet above the ground. the initial velocity is 75 feet per second. Use the formula: h=-16t^2+vt+s. How long will it take for the ball to hit the ground?

Answers

Answer: Do the math, the positive solution

t = 5.0495 seconds (If it's wrong sorry, I havent done a problem like this one in awhile!)

Step-by-step explanation:

What value of x satisfies the equation 3x – 2 = 2x + 4?

Answers

Answer:

x = 6

Step-by-step explanation:

3x - 2 = 2x + 4

First, we need only 1 set of x, so I'll subtract the smallest x from the other.

-2x both sides.

x - 2 = 4

Next, add +2 to both sides. (In these types of questions always do the inverse!)

And so your answer is:

x = 6

Answer:

x = 6

Step-by-step explanation:

1. Add  2  to both sides of the equation

3x - 2 = 2x + 4

3x - 2 + 2 = 2x + 4 + 2

2. Simplify  

3x = 2x + 6

3. Subtract 2x from both sides of the Equation

3x - 2x = 2x  + 6 - 2x

4. Simplify

x = 6

Let a and b be real numbers where ab+0. Which of the following functions could represent the graph below?
O f(x) = x(x – a)3(x – b) 3
O f(x) = (x – a)2(x – 614
O f(x) = x(x – a) (x – 5)2
O f(x) = (x – a)5(x – b)

Answers

The following functions could represent the graph below then the correct option is B; y =  (x - a)^2 (x - b)^4.

What is graph ?

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

we have given that a and b are real numbers different than zero.

From the graph, we can see that the line touches the x-axis in two values.

Now, if we would have an equation such as:

y = x(x - a)^3 (x - b)^3

then when x = 0

y = 0(0-a)^3 (0-b)^3

y = 0

But in the graph, we can see that when x = 0, the value of y is different than zero,

(For example, if x > a and x < b we would have a negative value for y)

Then the correct option is B ;y =  (x - a)^2 (x - b)^4

Learn more about graphing functions here:

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Compare 4:10 and 12:20 using fractions. Which ratio is smaller? How do you know?

Answers

4:10 is smaller because:
times the whole ratio by two to get: 8:20 now we can compare it to 12:20 and so 8 < 12 so the first one is smaller
I think 12:20 is similar

Is 29/49 an interger

Answers

No, integers cannot be fractions or decimals.

Annabelle picked 65 apples at a local orchard. 40% of the apples were green apples. How many green apples did Annabelle picked

Answers

26 green apples

if you do 0.4 * 65 you get 26 which is 40% of 65

hope this helps!

9 unit percent change is 23, what is the 19th unit percent cahnge?

Answers

Answer:

42.40705%

Step-by-step explanation:

(1 - (23/100)^(19/9) = 1 + r/100

0.57593 = 1 + r/100

r = 42.40705%

Maggie's brother is 5 years younger than three times her
age. The sum of their ages IS 43.
How old is Maggie?

Answers

Answer:

Step-by-step explanation:

Let Maggie's age = x

The brother's age = 3x - 5

x + 3x - 5 = 43

4x - 5 = 43              Add 5 to both sides

4x - 5 + 5 = 43+5

4x = 48                  Divide by 4

4x/4 = 48/4

x = 12

Maggie = 12

Brother = 3*12 - 5

Brother = 36 - 5

Brother = 31

question 5. Write an equation of the line that passes through the points (-2, -6) and (4, 6).
Answer in slope-intercept form

Answers

Answer:

y=2x-2

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(6-(-6))/(4-(-2))

m=(6+6)/(4+2)

m=12/6

m=2

y-y1=m(x-x1)

y-(-6)=2(x-(-2))

y+6=2(x+2)

y=2x+4-6

y=2x-2

Note that the slope-intercept form is y=mx+b where m=slope and b=y-intercept.

please help me if you can​

Answers

A) 100 degrees (congruent angle)
B) 45 degrees (congruent angle)
C) 90 degrees (right angle)
D) 99 degrees (congruent angle)
E) 30 degrees (congruent angle)
F) 30 degrees (180-150=30, that is to find the other angle that is congruent to f)

Help I’ll give brainliest

Answers

Answer:

Is it 95 If it is give me brainliess

Step-by-step explanation:

The answer is 95 I want it

Graph y= 0.5x^2 - 4x +6 on the coordinate plane.

Vertex:

Is this considered a minimum or maximum point?

Axis of symmetry: x=

Roots: x= and x=

Answers

Answer:

V: (4, -2), min, Axis: x = 4, Roots 2 and 6

Step-by-step explanation:

Multiply everything x 2 to get rid of the decimal in front of x^2

2y = x^2 - 8x + 12

Factor

2y = (x - 6)(x - 2)

The roots are at 2 and 6.

The axis of symmetry is in the center between the roots, so it is x = 4.

Put 4 into the original equation to find y

y = 0.5(4*2) - 4(4) + 6

y = 8 - 16 + 6, y = -2  

Vertex is at (4, -2). It is a minimum because the graph opens up since x*2 is positive.

HELP ASAPPPPPPP!!!!!

Answers

you will do 7x2x2x3 then after u find the answer you will write it in a fraction form like for example if you get 64 which is the answer and u will write 6 over 4 and that is the answer.

EASY 25 POINTS

If you get in incorrect I will not mark you brainliest.

Answers

Answer:

whats the question bro

Step-by-step explanation:

Answer:

whats the question mate?

Step-by-step explanation:

Need help please if anyone one can help me now I will like that

Answers

Answer:

.

Step-by-step explanation:

Step-by-step equation

guys do you know 9 divided by 0.954 because when i calculate it , it shows this big number so can you put it in an short way?

Answers

Answer:

9.43

Step-by-step explanation:

You simply use the first couple digits of the solution your calculator gave you. (How many depends on the question you were asked)

Answer:

  9 23/53

Step-by-step explanation:

The fraction is not particularly nice. It can be written as ...

  9/0.954 = 9000/954 = 500/53 = 9 23/53

As a decimal, the fraction has a 13-digit repeat:

  [tex]9.\overline{4339622641509}[/tex]

Two numbers are in a ratio 11:7. If the smaller number is 700, what is the larger number? Pls tell with steps

Answers

Answer:

The larger number is [tex]1100[/tex]

Step-by-step explanation:

Let larger number be [tex]x[/tex]

We have

[tex]\frac{x}{700} =\frac{11}{7} \\\\x=100\times11\\\\=1100[/tex]

Answer:

The larger number is 1100.

Step-by-step explanation:

Solution :

Let the,

>> Larger number be 11x. >> Smaller number be 7x.

Now, According to the question :

[tex]\begin{gathered} \dashrightarrow\sf{Smaller \: number} = \tt{700} \end{gathered}[/tex]

[tex]\begin{gathered} \dashrightarrow\sf{7x}= \tt{700} \end{gathered}[/tex]

[tex]\begin{gathered} \dashrightarrow\sf{x}= \tt{700 \div 7} \end{gathered}[/tex]

[tex]\begin{gathered} \dashrightarrow\sf{x}= \tt{ \dfrac{700}{7} } \end{gathered}[/tex]

[tex]\begin{gathered} \dashrightarrow\sf{x}= \tt{\cancel{\dfrac{700}{7}}} \end{gathered}[/tex]

[tex]\begin{gathered} \dashrightarrow \sf{x}= \tt{100} \end{gathered}[/tex]

Hence, the value of x is 100.

Now, calculating the larger number :

[tex]\begin{gathered} \dashrightarrow\sf{Larger \: number} = \tt{11x} \end{gathered}[/tex]

[tex]\begin{gathered} \dashrightarrow\sf{Larger \: number} = \tt{11 \times 100} \end{gathered}[/tex]

[tex]\begin{gathered} \dashrightarrow\sf{Larger \: number} = \tt{1100} \end{gathered}[/tex]

Hence, the larger number is 1100

[tex]\rule{300}{1.5}[/tex]

What is the answer to this?

Answers

Answer:

option b.)y=1/4x-7/2.....

What is the velocity of a car that traveled total of 75 km north in 1.5 hours?

Answers

Answer:

hope this helped!

Step-by-step explanation:

75 km = 75000 m

1.5 hours = 5400 sec

Applying the formula

Velocity

=

75000 m

5400 s

=

13.89 m/s

please help meeeeeeeeeeeeeeeeeeee

ty

Answers

Answer:

A

Step-by-step explanation:

hope this helped

Answer:

4y = -3x - 8

Step-by-step explanation:

Please help question in pic

Answers

Answer:

7,3

Step-by-step explanation:

for every 5 it goes right it goes 4 up. 2,1+5,4=7,3

PLS SHOW ME HOW U GET THE ANSWER AND WILL GIVE BRAINLYEST

Answers

Answer:

38 degrees

Step-by-step explanation:

all triangles length added up are 180 degrees.

add 52 and 90 to get 142. Subtract to get 38 degrees.

6. Find the value of y.
5
16

Answers

3.59999
or 3.6
hopefully this helps you!

Work out the difference between 38.3 and 1.72​

Answers

Answer:

36.58

Step-by-step explanation:

38.3-1.72=36.58

The value of the expression 38.3 - 1.72 will be 36.58.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The numbers are given below.

38.3 and 1.72​

Then the difference between the numbers 6 and 1/3 will be given by putting a minus sign between them. Then we have

⇒ 38.3 - 1.72

⇒ 36.58

The value of the expression 38.3 - 1.72 will be 36.58.

More about the Algebra link is given below.

https://brainly.com/question/953809

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What is the most precise and accurate definition of perpendicular lines?

A. two lines in a plane with opposite reciprocal slopes

B. two lines in a plane with opposite slopes

C. two lines in a plane with reciprocal slopes

D. two lines in a plane with the same slope

Answers

Answer:

A. two lines in a plane with opposite reciprocal slopes

Step-by-step explanation:

Because, if you flip a slope and change the sign, you get an opposite reciprocal to the original slope, thus, forming perpendicular lines.

Idrissa collected pennies in a fundraiser. He measured the mass of all the pennies he collected to be2,400 grams. Two pennies put together have a mass of 5 grams. How much money did Idrissa raise in
this fundraiser?

Answers

The total amount of pennies Idrissa raised in this fundraiser is = 960 pennies

The total mass of all the pennies = 2,400g

But two (2) pennies = 5g

Therefore, to calculate the total amount of pennies Idrissa raised you cross multiply.

That is: 2 pennies = 5g

x pennies = 2,400g

Making x the subject of formula,

[tex] x = \frac{2 \times 2400}{5} [/tex]

[tex]x = \frac{4800}{5} [/tex]

[tex]x = 960[/tex]

Therefore the total amount of pennies Idrissa raised in this fundraiser is = 960 pennies.

Learn more here:

https://brainly.com/question/294036

given that 5(x+k)=4x +. 20 and that x is positive show that k < 4

Answers

Answer: its 5k

Step-by-step explanation:

Solve for r.

√2/3r + 1 = 23

Answers

Answer:

2nd option

Step-by-step explanation:

[tex]\frac{\sqrt{2} }{3}[/tex] r + 1 = 23 ( subtract 1 from both sides )

[tex]\frac{\sqrt{2} }{3}[/tex] r = 22 ( multiply both sides by 3 to clear the fraction )

[tex]\sqrt{2}[/tex] r = 66 ( divide both sides by [tex]\sqrt{2}[/tex] )

r = [tex]\frac{66}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex] ( rationalising the denominator )

r = [tex]\frac{66\sqrt{2} }{2}[/tex] = 33[tex]\sqrt{2}[/tex]

Answer:

B) r=33*sqrt(2)

Step-by-step explanation:

sqrt(2)/3r+1=23

sqrt(2)/3r=23-1

sqrt(2)/3r=22

sqrt(2)r=22*3

sqrt(2)r=66

r=66/sqrt(2)

r=66*sqrt(2)/(sqrt(2)*sqrt(2))

r=(66*sqrt(2)/2

r=33*sqrt(2)

A triangle has side lengths of 2 feet, 5.4 feet, and 5 feet. The angle measures are 90 degrees, 73 degrees, 17 degrees. Another triangle has side lengths of 3 feet, 8.1 feet, 7.5 feet. The angle measures are 90 degrees, 73 degrees, 17 degrees. Are the triangles similar? If so, what is the scale factor going from the top triangle to the bottom triangle?

Answers

Answer:

Yes. The factor is 3/2 (=1,5)

Step-by-step explanation:

They have all the 3 angles congruent, so they are similar. You calculate the scale factor by dividing the hypotenuse (for example) of the second triangle by the hypotenuse of the first one.

Answer:

1) yes 2) 1.5

Step-by-step explanation:

have a nice day! <:

PLEASE HELP I NEED TO HAVE THIS DONE IN 30 MINUTES

Answers

Answer:

Yes it does. Because it's a linear graph, what Mena's it's a linear relationship, and linear relationships are proportional

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