Answer :
Given;
Admission fee for children is, f(C) = $4.
Admission fee for adult is, f(A) = $5.80.
Total number of people is, N = 296.
Total fees collected is, F = $1472.
The objective is to find the number of children and number of adults.
Consider the childrens as C and the adults as A.
Then, first population equation can be written as,
[tex]C+A=296[/tex]Then, first cost equation can be written as,
[tex]4C+5.8A=1472[/tex]Solve the two equations by multiplying the first equation by 4.
[tex]\begin{gathered} 4C+4A=1184 \\ 4C+5.8A=1472 \end{gathered}[/tex]On solving,
[tex]\begin{gathered} -1.8A=-288 \\ A=\frac{288}{1.8} \\ A=160 \end{gathered}[/tex]Substitute the value of A in equation (1) to finf the value of C.
[tex]\begin{gathered} C+160=296 \\ C=296-160 \\ C=136 \end{gathered}[/tex]Hence, the number of children is 136 and the number of adult is 160.
