Exercise 2 Page p47

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 percent proportion. 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 $\text{part}$ $a,$ the $\text{whole}$ $b,$ and the proportion in $\text{percent}.$ We know that the $\text{new}$ $\text{price}$ is $85\%$ of the $\text{regular}$ $\text{price},$ $\$9.99.$ Let's calculate how much the T-shirt cost without the sales tax. 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 $\text{whole}.$ By adding the sales tax to the new price we find how much we have to pay for the T-shirt. 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. The discount was about $\$1.50.$ The new price is the regular price minus the discount. 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 $a.$ Again we found that the final price is $\$9.$