Answer:
The number of adult tickets are 57.
Step-by-step explanation:
Given,
Total number of tickets = 156
Total money = $1077.60
Solution,
Let the number of adult be x and of child be y .
So, Total number of tickets = Number of adults + Number of child
[tex]\therefore x+y = 156\ \ \ \ \ \ equation\ 1[/tex]
Now, according to question;
Total money = [tex]Number\ of\ adults\times admission\ fee + Number\ of\ child\times admission\ fee[/tex]
[tex]\therefore x\times 9.70+y\times 5.30 = 1077.60\ \ \ \ \ \ equation\ 2[/tex]
On multiplying by 10 on both side, we get;
[tex]97x+53y=10776\ \ \ \ \ \ equation\ 3[/tex]
Now multiplying equation 1 by 53 then subtract it from equation 3, we get;
[tex](x+y)\times53 = 156\times53\\53x+53y=8268\\(97x+53y=10776)-(53x+53y=8268)\\44x=2508\\x=\frac{2508}{44} =57[/tex]
Since x is the number of adults,
Number of adults=57
Number of child = y = 156-57=99
Thus the number of adult tickets are 57.
