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 =
