Answer:
a.
Let x be the number of square yards of carpeting for which the total cost charged by the two companies will be the same.
We have an expression for the total cost of Country Carpets:
($22/ 1 yd^2)* (x yd^2) + $100
= $22*x+ $100
or 22x+ 100
We also have another expression for the total cost of City Carpets:
($25/ 1 yd^2)* (x yd^2)+ $70
= $25*x+ $70
or 25x+ 70
Now set the two expressions to be equal:
22x+ 100= 25x+ 70
⇒ 100- 70= 25x -22x
⇒ 30= 3x
⇒ 30/3= x
⇒ 10= x
The final answer for a is 10 square yards of carpeting~
b.
Let's assume that Mr. Shu wants to install carpeting for 1 square yard.
Country Carpets: $22*1+ $100= $122
City Carpets: $25*1+ $70= $95
Therefore, Mr. Shu will be likely to choose City Carpets if he wants to install carpeting for 1 square yard.
Now let's try x=11 (square yard):
Country Carpets= $22*11+ $100= $342
City Carpets= $25*11+ $70= $345
Therefore, Mr. Shu will be likely to choose Country Carpets if he wants to install carpeting for 11 square yard.
If you paid really close attention, you would notice that the price of City Carpets will be cheaper than the other when x is >0 and <10. At x=10, the price is equal. When x is >10, the price of Country Carpets will be cheaper than the other one.
So it depends:
If x were >0 and <10, Mr. Shu would be likely to choose City Carpets.
If x were 10, Mr. Shu could choose either Country Carpets or City Carpets.
If x were > 10, Mr. Shu would be likely to choose Country Carpets.
Hope this helps~
Step-by-step explanation:
