By making a four-step solving plan we want to find how much change we get when we buy a T-shirt and pay with a $10 bill. To use the four-step solving plan we need to Understand, Plan, Solve, and Check our solution to the exercise.
Understand
We are given the regular price of the T-shirt and are told that it is on sale. Also we learn that a sales tax is added to the price. We need to calculate the final price of the T-shirt. The difference between $10 and the final price is the change we receive.
Plan
The regular price is
$9.99 and it is on sale for
15% off. The new price is
100%−15%=85% of the regular price. To find the new price we use the .
ba=100p
When we know the new price we have to find how much the
6% sales tax equals. For this we will again use the percent proportion. We then subtract the sum of the new price and the sales tax from
10 to find how much change we get back.
Solve
The percent proportion states a relationship between the
part a, the
whole b, and the in
percent.
ba=100p
We know that the
new price is
85% of the
regular price, $9.99. Let's calculate how much the T-shirt cost without the sales tax.
ba=100p
9.99a=10085
a≈8.49
A sales tax of
6% is then added to this price. We find the sales tax by using the percent proportion and using the new price as the
whole.
ba=100p
8.49a=1006
a≈0.51
By adding the sales tax to the new price we find how much we have to pay for the T-shirt.
8.49+0.51=9.00
We have to pay
$9 for the T-shirt. If we give the cashier a
$10 bill, we will receive
$10−$9=$1 change.
Check
We now want to check our solution. The regular price is about
$10. We then got
15% off because it was on sale.
15% of 10=1.5
The discount was about
$1.50. The new price is the regular price minus the discount.
$10−$1.50=$8.50
With a sales tax of
6% added to that we can calculate the final price as
100%+6%=106% of
$8.50.
Let's use the percent proportion in which we substitute
b=8.50 and
p=106 into the formula and then solve for
a.
ba=100p
8.50a=100106
8.50a=5053
a=5053(8.50)
a=9.01
a≈9
Again we found that the final price is
$9.