Carpet plus installs carpet for $100 plus $8 per square yard of carpet. Carpet World charges $75 for installation and $10 per square yard of carpet. Find the number of square yards of carpet for which the cost including carpet and installation is the same.

Please help me solve this and show your work pleas and thank you.

100+8x = 75+10x

100-75 = 10x-8x
25 = 2x
/2 /2
12.5 = x

If you order 12.5 squares, the cost will be the same!!!

One shuttle service charges $10 for pickup and $0.10 per mile .the other shuttle service has no pickup fee but charges $0.35 per mile .find the number of miles for which the cost of the shuttle services is the same

To find the number of square yards of carpet for which the cost including carpet and installation is the same for Carpet Plus and Carpet World, we need to set up an equation and solve for the unknown variable.

Let's assume the number of square yards of carpet is represented by 'x'.

For Carpet Plus:
Cost for carpet = $8 per square yard * x
Cost for installation = $100
Total cost for Carpet Plus = Cost for carpet + Cost for installation = $8x + $100

For Carpet World:
Cost for carpet = $10 per square yard * x
Cost for installation = $75
Total cost for Carpet World = Cost for carpet + Cost for installation = $10x + $75

Since we want to find the number of square yards of carpet for which the cost is the same, we can set up an equation:

$8x + $100 = $10x + $75

Now, let's solve for 'x':

$8x - $10x = $75 - $100
-2x = -$25
x = -$25 / -2
x = 12.5

Therefore, the number of square yards of carpet for which the cost including carpet and installation is the same is 12.5 square yards.

The cost will be the same so its 12.5

12.5 yd squared