Question

Troy sold 28 bags of popcorn and 40 candy bars and made $282. Jake sold 17 bags of popcorn and 20 bags of candy and made $160.50. What was the cost of a bag of popcorn?

Answer 1

One bag of popcorn would cost $6.50

To solve this, we can set up equations:
28p+40c=$282
17p+20c=$160.50

To solve this system, we would need to make either the candy bars the same or the bags of popcorn the same. Since we are solving for bags of popcorn, we will make the candy bars the same:
20(28p+40c=$282)
40(17p+20c=$160.50)

Which would give you:
560p+800c=$5,640
680p+800c=$6,420

Subtract them:
 (680p+800c=$6,420)
-(560p+800c=$5,640)
_________________
120p=$780

Now divide by 120 to get the price of one bag of popcorn:
120p=$780
_________
       120

p=$6.50