a landscaper bought some decorative cement blocks from a landsccaping supplier. the supplier charged 5% sales tax and the total came to $315. without the tax, the landscaper could have bought 6 more blocks for the same total cost. how many blocks did the landscaper buy?

Answer 1

If there were n bricks at price p, then we know that

1.05np = 315
(n+6)p = 315

Now just eliminate p and solve for n.

Answer 2

number of blocks --- x
cost per block --- y
1.05xy = 315
xy = 300

without sales tax the cost would have been

(x+6)y = 315

so divide the two equations:
( (x+6)y)/(xy) = 315/300
(x+6)/x = 21/20
21x = 20x + 120
x = 120 , then y = 2.5

He bought 120 blocks at $2.50 each

check:
120(2.5)(1.05) = 315
with no tax:
126(2.5) = 315 , he could have bought 6 more, yeahh