A movie theater is selling only one size of popcorn and one size of soft drink. Jason purchased 2 popcorns and 3 soft drinks for a total of $23. Ann purchased 3 popcorns and 4 soft drinks for a total of $32.50. How much does a soft drink cost?

A soft drink costs $4

Step-by-step explanation: First of all, we shall represent popcorns by letter p, and soft drinks by letter d. Therefore if Jason purchased 2 popcorns and 3 soft drinks for $23, we can express this as follows;

2p + 3d = 23

Also, if Ann purchased 3 popcorns and 4 softdrinks for $32.5, we can write this too as;

3p + 4d = 32.5

We now a pair of simultaneous equations

2p + 3d = 23 ———(1)

3p + 4d = 32.5 ——-(2)

We shall apply the elimination method since all the unknown variables have coefficients greater than 1. To do this, multiply equation (1) by 3 and multiply equation (2) by 2 {to eliminate the p variable.

2p + 3d = 23 ———x3

3p + 4d = 32.5 ——-x2

6p + 9d = 69 ———(3)

6p + 8d = 65 ———(4)

Subtract equation (4) from equation (3)

{6p - 6p} + {9d - 8d} = 69 - 65

d = 4

Having calculated that, we can now calculate p. Substitute for the value of d into equation (1)

2p + 3(4) = 23

2p + 12 = 23

Subtract 12 from both sides of the equation

2p = 11

Divide both sides of the equation by 2

p = 5.5

Therefore, d = 4 and p = 5.5

That means soft drinks (d) cost $4 each.

add 5 subtract 1

step-by-step explanation: