Study Guide

Ratios & Percentages - Percentages in the Real World

Percentages in the Real World

You'll use percentages for the rest of your life. That's a promise, not a threat. Percentages are used to figure out how much money we need to put 10% down on an apartment, how much we'll pay for the 6.25% sales tax on our new monster truck, and how much we save when the camera we're buying is on clearance for 57% off.

Sample Problem

Sales tax in certain parts of the state of California is 9.25%. After shopping at a Shmarget in Shmaguna Beach, our purchases came to \$62.75, before tax. How much do we end up paying, including tax?

To figure this one out, we just need to add the 9.25% sales tax to the total. First find 9.25% of \$62.75.

Let's go with the equation method this time. To convert 9.25% to a decimal, we slide the decimal point to the left two places.

9.25% = 0.0925

Then we translate "What is 9.25% of \$62.75?" into an equation.

x = 0.0925 × 62.75

A little calculator work gives us the answer.

x = 5.804375

We're dealing with money, so we'd better round that to the nearest cent.

x ≈ \$5.80

But wait, we're not done yet. That's our sales tax, but we want to know the total cost of our Shmarget bill. We still need to add the sales tax to the total.

\$5.80 + \$62.75 = \$68.55

That's our total bill. Thanks for shopping at Shmarget!

Side note: we could've also solved this problem using proportions instead. To find 9.25% of \$62.75 this way, we'd set up two ratios like so:

Then we multiply both sides of the equation by (100)(62.75) to get rid of those denominators. After canceling the 100s on the left and canceling the 62.75s on the right, we get:

(62.75)(9.25) = 100x

580.4375 = 100x

Dividing both sides by 100 gives us x = 5.804375, so our sales tax is x ≈ \$5.80, same as before. Adding that to the subtotal still gives us a grand total of \$68.55. Either way works.

Check out the other examples here for just a few places where percents will cross your path: commission, discounts, sales tax, bank accounts, and tips at restaurants.