Dan buys 2 large popcorns and 4 small drinks fot $22. Tom buys 3 large popcorns and 2 small drinks for $21. Find the cost of each

Question

This is a algebra 2 word problem for solving systems

Answer 1

Let's start by defining our variables:

p = popcorn

d = drinks

 

Here's what we know:

2p + 4d = 22

3p + 2d = 21

 

I look at that 2d and 4d and see an easy elimination. By multiplying the second equation by -2, we can eliminate the d and solve for p:

 2p + 4d =  22
-6p - 4d = -42

 

-4p = -20

Divide both sides by -4, and:

p = 5

 

So popcorn costs $5. Using that, we can solve for d:

2 * 5 + 4d = 22

10 + 4d = 22

4d = 12

d = 3

 

So small drinks are $3.

Let's check our answer by putting the values into the second problem:

3 * 5 + 2 * 3 = 21

15 + 6 = 21

21 = 21