Question

5 plates and 4 cups cost 21.20 dollars. 6 plates and 5 cups cost 25.70 dollars. Each plate costs the same amount as the other plates, and each cup costs the same amount as the other cups. What is the cost of 1 plate? What is the cost of 1 cup?

Answer 1

x = cost of a plate = $3.2

y = cost of a cup = $1.3

Explanation:

Let

x = cost of a plate

y = cost of a cup

5x + 4y = 21.20 (1)

6x + 5y = 25.70 (2)

Multiply (1) by 5 and 2 by 4

25x + 20y = 106 (3)

24x + 20y = 102.8 (4)

Subtract (3) from (4) to eliminate y

25x - 24x = 106 - 102.8

x = 3.2

Substitute x = 3.2 into (1)

5x + 4y = 21.20 (1)

5(3.2) + 4y = 21.20

16 + 4y = 21.20

4y = 21.20 - 16

4y = 5.2

y = 5.2/4

y = 1.3

x = cost of a plate = $3.2

y = cost of a cup = $1.3