We want to determine which backpack was the better buy. Let's find the sale price of each backpack, starting with Mary's backpack. We can find the dollar amount of the discount using the percent equation.

part = percent \times whole

We are given that Mary's backpack originally cost

$ 65

and was discounted

25 % .

Let

m

represent the dollar amount of the discount.

m = 25 % \times $ 65

We need to write the percent as a decimal before we can solve the equation that we created. We can do this by ignoring the percent symbol and moving the decimal point two places to the left.

Therefore,

25 %

is equal to

0.25 .

m = 25 % \times $ 65 ⇓ m = 0.25 \times $ 65

Now we can solve the equation for

m .

For simplicity, we will ignore the units for now.

m = 0.25 \times 65

UseCalc

Use a calculator

m = 16.25

We got that

m = 16.25

is a solution to the equation. This means that the dollar amount of the discount is

$ 16.25 .

Now we can calculate the sale price of Mary's backpack by subtracting

$ 16.25

from the regular price.

$ 65 - $ 16.25 = $ 48.75

The sale price of Mary's backpack was

$ 48.75 .

Now let's find the sale price of Roberto's backpack. We know that his backpack originally cost

$ 75

and was on sale for

30 %

off the original price. Let

r

represent the dollar amount of the discount.

part = percent \times whole ⇓ r = 30 % \times $ 75

Like before, we will write the percent as a decimal by ignoring the percent symbol and moving the decimal point two places to the left.

r = 30 % \times $ 75 ⇓ r = 0.3 \times $ 75

Then we can solve the equation for

r .

r = 0.3 \times 75

UseCalc

Use a calculator

r = 22.5

Ricardo's backpack was discounted by

$ 22.50 .

Let's calculate the sale price of the backpack by subtracting

$ 22.50

from the regular price.

$ 75 - $ 22.50 = $ 52.50

The sale price of Roberto's backpack was

$ 52.50 .

Finally, let's compare the sale prices.

Mary ’ s backpack $ 48.75 < Roberto ’ s backpack $ 52.50

As we can see, Mary's backpack was the better buy because it was cheaper.

Exercise