Answer:
The cost of the carpet at Magic Carpet is: 90 + 9*(area of carpet)
The cost of carpet at Carpeteria is: 50 + 13*(area of carpet)
The algebraic expression for which the cost is the same is: 90 + 9*(area of carpet) = 50 + 13*(area of carpet)
The area of carpet for which the cost is the same is: 10 square yard
Step-by-step explanation:
6a) The cost for magic carpet:
This company charges a fixed fee and a price for each square yard of carpeting, therfore the expression for the cost is:
cost = 90 + 9*a
Where a is the area of carpet to be installed.
6)b) The cost for Capeteria:
This company also charges a fixed fee and a price for each square yard of carpeting, so the expression is:
cost = 50 + 13*a.
6) c) The algebraic expression for the cost to be the same in both stores:
90 + 9*a = 50 + 13*a
6) d) We need to solve the expression above for a:
50 + 13*a = 90 + 9*a
13*a - 9*a = 90 - 50
4*a = 40
a = 40/4 = 10
