i did not get a response so i am rewording question . please help if you can. thanks ann
store A charges 9.75% tax
store B charges 7.25% tax
If a shopper's pre tax receipt is between $11.57 and $81.43, write a compound inequality that describes the difference in taxes paid for the two locations( to the nearest cent).
I wrote 11.57 less than or equal to y less than or equal to 81.43.
I could not figure out how to handle tax.
if y is the pre-tax price
11.57 <= y <= 81.43
A: 11.57*.0975 <= tax <= 81.43*.0975
B: 11.57*.0725 <= tax <= 81.43*.0725
If you subtract B from A, to get the difference in taxes,
A-B: 11.57*.025 <= taxdiff <= 81.43*.025
or
0.29 <= taxdiff <= 2.04
thank you very much for your help anonymous ann
To find the difference in taxes paid for the two locations, we need to determine the tax amount for each store and then subtract them.
Let's start by calculating the tax amount for store A. Tax is usually calculated by multiplying the pre-tax amount by the tax rate. In this case, the tax rate for store A is 9.75%. To find the tax amount, we can use the formula:
Tax amount = Pre-tax amount * Tax rate
Similarly, for store B with a tax rate of 7.25%, we can calculate the tax amount using the same formula.
Now, to write a compound inequality that describes the difference in taxes paid, we can subtract the tax amount for store B from store A and set a range within which this difference falls.
Let's represent the difference in taxes as 'd'. The compound inequality can be written as:
11.57 * 9.75% - 81.43 * 9.75% ≤ d ≤ 11.57 * 7.25% - 81.43 * 7.25%
Simplifying this inequality further, consider the tax amount paid at store A as X and store B as Y:
11.57 * 0.0975 ≤ X - Y ≤ 81.43 * 0.0975
11.28 ≤ X - Y ≤ 7.91
Therefore, the compound inequality that describes the difference in taxes paid for the two locations is:
11.28 ≤ d ≤ 7.91
Keep in mind that this is an approximation to the nearest cent, so the exact values may vary slightly.