Answer :
Given:
At the city museum, child admission is $5.80 and adult admission is $9.00.
Let the number of children's tickets = x
And the number of the adult tickets = y
on Monday 162 tickets were sold ⇒ x + y = 162
The tickets were sold for a total sale of $1176.40 ⇒ 5.8x + 9y = 1176.40
So, we have the following system of equations:
[tex]\begin{gathered} x+y=162\rightarrow(1) \\ 5.8x+9y=1176.40\rightarrow(2) \end{gathered}[/tex]From equation (1) x = 162 - y
substitute (x) into equation (2)
[tex]5.8(162-y)+9y=1176.40[/tex]Solve the equation to find (y):
[tex]\begin{gathered} 5.8*162-5.8y+9y=1176.4 \\ 939.6+3.2y=1176.4 \\ 3.2y=1176.4-939.6 \\ 3.2y=236.8 \\ \\ y=\frac{236.8}{3.2}=74 \end{gathered}[/tex]substitute (y) to find (x)
[tex]x=162-74=88[/tex]So, the answer will be:
The number of children tickets = 88
The number of adult tickets = 74