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?

Question

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?

Answer 1

Amount of tax=315*(5/105)=15

Cost of 6 blocks=15/6=2.5 each block
Number of blocks purchased = (315-15)/2.5
=120

Answer 2

To solve this problem, let's assume the cost of each decorative cement block before tax is "x" dollars.

Without tax, the landscaper could have bought 6 more blocks for the same total cost. This means that the cost of 6 blocks is equal to the tax charged on the original purchase.

We know that the sales tax charged by the supplier is 5% of the total cost. So we can calculate the tax amount by multiplying the total cost by 5/100:

Tax = 5/100 * Total cost

Let's denote the total cost of the purchase as "T". Therefore, the tax amount can be expressed as:

Tax = 5/100 * T

Now, we know that the cost of 6 blocks is equal to the tax amount, which we can represent as:

6x = 5/100 * T

Now, to find the value of "T", we need to subtract the tax amount from the total cost:

Total cost = T - Tax

Substituting the value of Tax from the previous equation:

Total cost = T - (5/100 * T)
Total cost = T(1 - 5/100)
Total cost = T(95/100)
Total cost = 0.95T

We are given that the total cost is $315, so we can now solve for "T":

0.95T = $315

Dividing both sides of the equation by 0.95:

T = $315 / 0.95
T ≈ $331.58

Now that we know the total cost "T", we can calculate the cost of each block:

x = T / Number of blocks
x = $331.58 / Number of blocks

Since the landscaper could have bought 6 more blocks for the same total cost, the equation becomes:

x = $331.58 / (Number of blocks + 6)

Setting both equations equal to each other:

$331.58 / Number of blocks = $331.58 / (Number of blocks + 6)

To simplify the equation, we can cross multiply:

(Number of blocks + 6) * $331.58 = $331.58 * Number of blocks

Expanding:

$331.58 * Number of blocks + $331.58 * 6 = $331.58 * Number of blocks

Subtracting $331.58 * Number of blocks from both sides:

$331.58 * 6 = $331.58 * Number of blocks - $331.58 * Number of blocks

Simplifying:

$331.58 * 6 = 0

This equation doesn't make sense as it states that $331.58 * 6 is equal to $0, which is not possible. Therefore, there is no valid solution to this problem based on the information provided. It is likely that there is missing or incorrect information in the question.