a landscaper bought same decorative cement blocks from a landscaping 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?
Cost = Po + 0.05Po = $315
1.05Po = 315
Po = $300 = Initial price.
(315-300)/6blks = $2.50/blk
300/(2.50/blk) = 120 Blocks bought.
To solve this problem, we need to set up an algebraic equation. Let's denote the cost of each decorative cement block as "x" and the number of blocks bought as "n".
According to the problem statement, when the sales tax of 5% is added, the total cost is $315. Therefore, the equation can be written as:
(1 + 0.05)nx = 315
Simplifying the equation:
1.05nx = 315
Now, we are given that without the tax, the landscaper could have bought 6 more blocks for the same total cost. This implies that the total cost would be the same, but the number of blocks would be n + 6. Therefore, we can write another equation:
nx + 6x = 315
Simplifying the equation:
nx + 6x = 315
Now, we have a system of two equations:
1.05nx = 315
nx + 6x = 315
To solve this system of equations, we can use substitution or elimination method. Let's use substitution method:
From the first equation, we can solve for nx as follows:
1.05nx = 315
nx = 315 / 1.05
nx ≈ 300
Now, we substitute nx = 300 in the second equation:
300 + 6x = 315
Simplifying the equation:
6x = 315 - 300
6x = 15
x = 15 / 6
x ≈ 2.5
Since x represents the cost of each decorative cement block, and it's not possible to have a fraction of a block, we can conclude that the cost of each block is approximately $2.50.
Now, we can find the number of blocks bought by dividing the total cost ($315) by the cost of each block ($2.50):
n = 315 / 2.5
n = 126
Therefore, the landscaper bought 126 decorative cement blocks.