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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?

What System Of Equations Would You Use To Solve The Problem BelowThe Admission Fee For An Amusement Park Is 12 For Adults And 650 Forchildren One Weekend 2904 P class=

Sagot :

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:

[tex]\begin{gathered} \frac{-5.50c}{-5.50}=\frac{-7722}{-5.50} \\ \\ c=1404 \end{gathered}[/tex]

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 =

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