for a school fundraiser troy sold 28 bags of popcorn and 40 candy bars and made 282. jake sold 17 bags of popcorn and 20 candy b ars and made 160.50. what was the cost of a bag of popcorn
2 answers:
Assuming the cost of a bag of popcorn is p and that of candy bars is b, then; Troy ; 28p +40b = 282 Jake; 17b + 20b = 160.50 Solving the two equations simultaneously, 20(28p +40b =282) 40(17p + 20b =160.5) we get; 560p +800b = 5640 680p + 800b = 6420 subtracting to eliminate b; -120p= -780 p = 6.50 Replacing the value of p in either equation to get b; 17 (6.5) +20b =160.5 20b = 50 b = 2.50 Therefore the cost of a bag of popcorn is 6.50
Let x and y be the cost of each of the bags of popcorn and candy bars, respectively. With this, the total amount that Troy raised can be expressed as, 28x + 40y = 282 In similar manner, we may also express the amount raised by Jake raised is, 17x + 20y = 160.50 The system of linear equations is rewritten below. 28x + 40y = 282 17x + 20y = 160.50 The values of x and y from the equation are 6.5 and 2.5. Answer: popcorn = $6.5 candy bars = $2.5
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