Question

What system of equations would you use to solve the problem below?The admission fee for an amusement park is $12 for adults and $6.50 forchildren. One weekend, 2904 people paid admission for the amusement park,and the park made $27,126. How many adults and how many children paid togo to the amusement park that weekend?

Answer 1

Given:

Admission fee for adults = $12

Admission fee for children = $6.50

Number of people admitted = 2904

Amount made = $27,126

Let's find the number of children and adults paid to go to the amusement park that weekend.

Let a represent the number of adults

Let c represent the number of children.

The equation represents the total number of people:

a + c = 2904

The equation below represents the total amount made:

12a + 6.50c = 27126

Hence, we have the set of equations:

a + c = 2904

12a + 6.50c = 27126

Let's solve for a and c.

Solve the equations simulteneously using substitution method.

Rewrite equation 1 for a:

a = 2904 - c

Substitute the (2904 - c) for a in the second equation:

12(2904 - c) + 6.50c = 27126

Apply distributive property:

12(2904) + 12(-c) + 6.50c = 27126

34848 - 12c + 6.50c = 27126

34848 - 5.50c = 27126

Subtract 34848 from both sides:

34848 - 34848 - 5.50c = 27126 - 34848

-5.50c = -7722

Divide both sides by -5.50:

`\begin{gathered} (-5.50c)/(-5.50)=(-7722)/(-5.50) \\ \\ c=1404 \end{gathered}`

Substitue 1404 for c in either of the equations.

Take eqaution 1:

a + c = 2904

a + 1404 = 2904

Subtract 1404 from both sides of the equation:

a + 1404 - 1404 = 2904 - 1404

a = 1500

Therefore, we have the solutions:

a = 1500

c = 1404

Number of adults = 1500

Number of children = 1404

ANSWER:

B. a + c = 2904

12a + 6.50c = 27126

Number of adults = 1500

Number of children =