Question

6 plates and 5 cups cost 23.80 dollars. 7 plates and 6 cups cost 28.00 dollars. Each plate costs the same amount as the other plates, each cup costs the same amount as the other cups. What is the cost of one plate? What is the cost of 1 cup?

Answer 1

c = $1.4

p = $2.8

Explanation:

two equations can be derived from the question

6p + 5c = 23.80 equation 1

7p + 6c = 28 equation 2

p = plates

c - cups

multiply equation 1 by 7 and equation 2 by 6

42p + 35c = 166.60 equation 3

42p + 36c = 168 equation 4

subtract equation 3 from 4

c = 1.4

substitute for c in equation 1

6p + 5(1.4) = 23.80

p = (23.80 - 7) / 6

p = 2.8