System Equation Word Problem

Question

The concession stand at a local festival sold pretzels and drinks. One customer bought 4 pretzels and 5 drinks for $30.75. Another customer paid $20 for 3 pretzels and 2 drinks and received $3.50 in change. How much would a customer pay if they bought a pretzel and a drink?

Let x = a pretzel

Answer 1

4P + 5D = 30.75

3P+ 2D = 16.50

multiply 1st by 3, 2nd by 4 and subtract them to eliminate one variable. then solve for the other

12P + 15D = 92.25

12P + 8D = 66.00

7D = 26.25

D = $3.75

3P =16.50 - 7.50 = 9

P = 9/3 = $3.00

P+D = $6.75