Answer: 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.
