Kelly took clothes to the cleaners 3 times last month. First, she brought 4 shirts and 1 pair of slacks and paid11.45. Then she brought 5 shirts, 3 pairs of slacks, and 1 sports coat and paid 27.41. Finally, she brought 5 shirts and 1 sports coat and paid 16.94. How much was she charged for each shirt, each pair of slacks, and each sports coat?
Let s be the cost of shirts, p be the cost of slacks, and c be the cost of sports coats. We're given:
p = 11.45 - 4s
Rearrange (3)by subtracting 5s from each side:
c = 16.94 - 5s
Take those rearranged equations, and plug them into (2):
5s + 3(11.45 - 4s) + (16.94 - 5s) = 27.41
Multiply through:
5s + 34.35 - 12s + 16.94 - 5s = 27.41
Group like terms using our equation calculator and we get:
s = 1.99 <-- Shirt Cost
Plug s = 1.99 into modified equation (1):
p = 11.45 - 4(1.99)
p = 11.45 - 7.96
p = 3.49 <-- Slacks Cost
Plug s = 1.99 into modified equation (3):
c = 16.94 - 5(1.99)
c = 16.94 - 9.95
c = 6.99 <-- Sports Coat cost
Let s be the cost of shirts, p be the cost of slacks, and c be the cost of sports coats. We're given:
- 4s + p = 11.45
- 5s + 3p + c = 27.41
- 5s + c = 16.94
p = 11.45 - 4s
Rearrange (3)by subtracting 5s from each side:
c = 16.94 - 5s
Take those rearranged equations, and plug them into (2):
5s + 3(11.45 - 4s) + (16.94 - 5s) = 27.41
Multiply through:
5s + 34.35 - 12s + 16.94 - 5s = 27.41
Group like terms using our equation calculator and we get:
s = 1.99 <-- Shirt Cost
Plug s = 1.99 into modified equation (1):
p = 11.45 - 4(1.99)
p = 11.45 - 7.96
p = 3.49 <-- Slacks Cost
Plug s = 1.99 into modified equation (3):
c = 16.94 - 5(1.99)
c = 16.94 - 9.95
c = 6.99 <-- Sports Coat cost