For this case, the first thing we must do is define variables.
We have then:
x: number of square yards of carpeting.
y: total cost.
We now write the equation for each store.
We have then:
For The magic carpet:
[tex] y = 9x + 90 [/tex]
For The carpeterias:
[tex] y = 13x + 50 [/tex]
By the time the price is the same we have:
[tex] 13x + 50 = 9x + 90 [/tex]
From here, we clear the value of x.
We have then:
[tex] 13x-9x = 90-50 [/tex]
[tex] 4x = 40 [/tex]
[tex] x = \frac{40}{4} [/tex]
[tex] x = 10 [/tex]
Answer:
For 10 square yards the cost is the same in both stores.
