Question

score: 0 of 1 point
the admission fee at an amusement park is $3.25 for children and $5.40 for adults. on a certain day, 309 people entered the park, and the admission fees collected totaled $1316. how many children and how many adults were admitted?
number of children: enter your answer
number of adults: enter your answer
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Explanation:

Step1: Define variables

Let \( x \) be the number of children and \( y \) be the number of adults. We have two equations:

1. \( x + y = 309 \) (total number of people)
2. \( 3.25x + 5.40y = 1316 \) (total admission fees)

From the first equation, we can express \( x \) as \( x = 309 - y \).

Step2: Substitute into the second equation

Substitute \( x = 309 - y \) into \( 3.25x + 5.40y = 1316 \):
\[
3.25(309 - y) + 5.40y = 1316
\]
Expand the left side:
\[
3.25\times309 - 3.25y + 5.40y = 1316
\]
Calculate \( 3.25\times309 = 994.25 \):
\[
994.25 + 2.15y = 1316
\]

Step3: Solve for \( y \)

Subtract 994.25 from both sides:
\[
2.15y = 1316 - 994.25
\]
\[
2.15y = 321.75
\]
Divide both sides by 2.15:
\[
y = \frac{321.75}{2.15} = 150
\]

Step4: Solve for \( x \)

Substitute \( y = 150 \) into \( x = 309 - y \):
\[
x = 309 - 150 = 159
\]

Answer:

Number of children: \( 159 \)
Number of adults: \( 150 \)