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.

\frac{a}{b} = \frac{p}{1 0 0}

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 proportion in

percent .

\frac{a}{b} = \frac{p}{1 0 0}

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.

\frac{a}{b} = \frac{p}{1 0 0}

SubstituteII

$b = 9.99$ , $p = 85$

\frac{a}{9 . 9 9} = \frac{8 5}{1 0 0}

▼

Solve for

a

MultEqn

$LHS \cdot 9.99 = RHS \cdot 9.99$

a = \frac{8 5}{1 0 0} (9.99)

UseCalc

Use a calculator

a = 8.4915

RoundDec

Round to $2$ decimal place(s)

a \approx 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 .

\frac{a}{b} = \frac{p}{1 0 0}

SubstituteII

$b = 8.49$ , $p = 6$

\frac{a}{8 . 4 9} = \frac{6}{1 0 0}

▼

Solve for

a

MultEqn

$LHS \cdot 8.49 = RHS \cdot 8.49$

a = \frac{6}{1 0 0} (8.49)

UseCalc

Use a calculator

a = 0.5094

RoundDec

Round to $2$ decimal place(s)

a \approx 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 .

\frac{a}{b} = \frac{p}{1 0 0}

SubstituteII

$b = 8.50$ , $p = 106$

\frac{a}{8 . 5 0} = \frac{1 0 6}{1 0 0}

▼

Solve for

a

ReduceFrac

$\frac{a}{b} = \frac{a / 2}{b / 2}$

\frac{a}{8 . 5 0} = \frac{5 3}{5 0}

MultEqn

$LHS \cdot 8.50 = RHS \cdot 8.50$

a = \frac{5 3}{5 0} (8.50)

UseCalc

Use a calculator

a = 9.01

RoundInt

Round to nearest integer

a \approx 9

Again we found that the final price is

$ 9 .

Exercise