Answer:
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
Answer:
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
