Answer:
The bag of popcorn costs $6.50
Explanation:
Let the price of a box of cookies be C.
Let the price of a bag of popcorn be P.
Ava sold 10 boxes of cookies and 8 bags of popcorn and raised $102. This implies that:
10C + 8P = 102 ___________(1)
Greg sold 4 boxes of cookies and 12 bags of popcorn and raised $98. This implies that:
4C + 12P = 98 ___________(2)
We now have two simultaneous equations:
10C + 8P = 102 ___________(1)
4C + 12P = 98 ____________(2)
Multiply (1) by 4 and multiply (2) by 10:
4 * (10C + 8P = 102)
10 * (4C + 12P = 98)
We get:
40C + 32P = 408 ___________(3)
40C = 120P = 980 __________(4)
Subtract (3) from (4):
40C + 120P = 980
- (40C + 32P = 408)
88P = 572
=> P = 572 / 88 = $6.50
Therefore, the bag of popcorn costs $6.50.