Wesley is making a patio from stones of two sizes 5 inches wide and 10 inches wide. he wants to begin and end his pattern with a 10 inch stone so there will be one more 10 inch stone than of the 5 inch stones. his patio will be 175 inches wide. how many 10 inch stones will he need for one row?

12 10" stones are required.

Since Wesley is using 1 extra 10" stone. The formula is:
x(10 + 5) + 10 = 175

Distribute the x
10x + 5x + 10 = 175

Merge the x terms
15x + 10 = 175

Subtract 10 from both sides
15x = 165

Divide both sides by 15
x = 11

Now the value for x is the number of 10" and 5" stones, but DOES NOT count the extra stone at the end. So

The number of 5" stones is 11
The number of 10" stones is 11 + 1 = 12