Question

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 bars and made 160.50. what was the cost of a bag of popcorn

Answer 1

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

Answer 2

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