6 plates and 5 cups cost 32.10 dollars. 7 plates and 6 cups cost 37.70 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?

Plates are 2.80 Dollars and cups are 1.40 dollars

Step-by-step explanation:

Cups = c

Plates = p

6p + 5c = 23.80 ==> multiply by 6 ==> 36p + 30c = 142.80

7p + 6c = 28.00 ==> multiply by 5 ==> 35p + 30c = 140.00

Now use algebra to have the 30c be on one side and the rest on the other:

36p + 30c = 142.80 | -36p

30c = 142.80 - 36p

35p + 30c = 140.00 | -35p

30c = 140.00 - 35p

Now set them equal to each other about the 30c:

142.80 - 36p = 140.00 - 35p

Use algebra to solve for p:

142.80 - 36p = 140.00 - 35p | +36p

142.80 = 140.00 + p | - 140

2.80 = p

Go back to one of the "30c" equations and plug in the value for p:

30c = 140 - 35p

30c = 140 - 35(2.80)

30c = 140 - 98

30c = 42 | /30

c = 42/30

c = 1.4

the cost of 1 plate  $4.1

the cost of 1 cup $1.5

Step-by-step explanation:

6p + 5c = 32.10

7p + 6c=  37.70

Multiply the first by 6

Multiply the second by -5

and then ADD both

36p +30c = 192.6

-35p-30c =  -188.5   (30c is cancelled)

p = 4.1

4.1(6) +5c = 32.10

24.6 +5c = 32.10

5c = 7.5

c= 1.5

1.5(5) =7.5

24.6 + 7.5 = 32.10