5 plates and 4 cups cost 30.90 dollars. 6 plates and 5 cups cost 37.50 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?

the cost of one plate is $4.5

The cost of one cup is $2.1

Step-by-step explanation:

Let x represent the cost of 1 plate.

Let y represent the cost of 1 cup.

5 plates and 4 cups cost 30.90 dollars. It means that

5x + 4y = 30.9- - - - - - - -1

6 plates and 5 cups cost 37.50 dollars. It means that

6x + 5y = 37.5- - - - - - - -2

Multiplying equation 1 by 6 and equation 2 by 5, it becomes

30x + 24y = 185.4

30x + 25y = 187.5

Subtracting, it becomes

- y = - 2.1

y = 2.1

Substituting y = 2.1 into equation 1, it becomes

5x + 4 × 2.1 = 30.9

5x + 8.4 = 30.9

5x = 30.9 - 8.4

5x = 22.5

x = 22.5/5

x = 4.5

think about it deeply and passionately about this property

i am sorry