Use a percent proportion to find what percent of the taxable sales amount is $7.50.
B
b
Multiply the sales tax rate, written as a decimal, by the taxable portion of the total price p.
C
c
Create an inequality where the amount paid in the 5 % state is less than the 6.25 % state.
A
a
6.25 %
B
b
Inequality: p+0.0625(p-175)≤430
Solution: p≤415
C
c
Inequality: p+0.05p
Solution: p>875 Example prices: $945, $1200, and $1500.
Practice makes perfect
a
We are told that the tax applies only to the difference between the price of the item and $175. We can see from the receipt that the price of the suit is $295. This difference is the taxable amount.
295 - 175 = 120
We will now find what percent of this amount is 7.50.
This can be done using a percent proportion.
To find the possible prices p of coats that the shopper can afford we need to consider the sales tax. Since the shopper can spend at most $430, we can write an inequality for this situation.
p+Sales Tax≤$430
We are told that the sales tax applies only to the difference between the price p of the item and 175. We found in Part A that the tax rate is 6.25 %, which can be rewritten as the decimal value 0.0625.
Sales Tax = 0.0625(p-175)
We can use this to rewrite our inequality.
p+0.0625(p-175)≤430
Let's solve this inequality for p.
Any item costing more than $875 will be cheaper if purchased in the state with a flat 5 % sales tax rate. Three example prices are $945, $1200, and $1500.
