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Hi, can you please help me solve this world problem for the second part of my homework?
The boy scouts sold $894 worth of tickets for their spaghetti dinner. Adult tickets cost $8 each and children’s tickets
cost $5 each. If they sold 132 tickets, how many adult tickets and how many children’s tickets were sold?
a. Write a system of equations which represents this problem.
b. Use substitution to solve.
c. Clearly state the answer to the question.
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Let "x" be the number of adult tickets.
Let "y" be the number of children's tickets.
Then
x + y = 132, (1) and
8x + 5y = 894. (2)
From equation (1), express x = 132 - y and substitute it into equation (2). You will get
8*(132-y) + 5y = 894.
It is a single equation for one unknown y. Simplify and solve it for y:
1056 - 8y + 5y = 894,
-3y = 894 - 1056,
-3y = -162 ----> y = = 54.
So, 52 children's tickets were sold.
Then the number of adults tickets was 132 - 54 = 78.
Answer. 78 adult tickets and 54 children's tickets were sold.
Check. 78*8 + 54*5 = 894 dollars./ Correct !!
Solved.