Percentages in the Real World at a Glance

You landed a fabulous summer job working as a sales assistant at Shmacy's. You earn a 4% commission on every sale you make, in addition to your wage of $8.50/hour. After a long seven-hour shift, your sales totaled $1250. What are your total earnings for that shift?

First, you earn $8.50/hour and worked seven grueling hours. That would total $8.50 × 7 = $59.50.

In addition you earned 4% of your sales, or 4% of $1250. Using the proportion method, this would be set up as:

Now multiply both sides by (100)(1250) to drop those denominators.

And divide by the coefficient (100).

So, you earned $50 in commission.

Combining your commission and wages, you earned a total of $59.50 + $50 = $109.50 in one day. Cha-ching!

The Sports Shmauthority is having an amazing sale on all of their winter gear, 65% off the regular price. You find the snowboarding jacket that you've been wanting for the past year. It was $220 before the sale. How much is it now?

Nice find! Okay, so this jacket is 65% off of $220. We first need to find what 65% of $220 is. Let's translate that into an equation:

What (x) is (=) 65% (0.65) of (multiply) 220?

x = 0.65 × 220

Now, solve the equation.

x = 0.65 × 220 = 143

The tricky part about discounts is remembering that this is the price off, not the price you pay. To find the sale price, just subtract the amount off from the original price.

$220 – $143 = $77

That awesome jacket is only $77! Score!

All sweaters are 30% off of the original price. You, being the clever shopper you are, also have a coupon for 15% off any item, including sale items. How much does a $75 sweater cost?

Now, you might be tempted to combine these two percentages and say that the sweater is 45% off, but that won't work. You can't combine discounts like that.

First take 30% off to find the sale price, then take 15% off the sale price to find the amount you'll pay, including your coupon.

30% of $75 = 0.3 × $75

0.3 × $75 = $22.50

This is the amount off, so we need subtract this amount from the original price.

$75 – $22.50 = $52.50

That's the sale price, but you still want to use that coupon. Now we need to take 15% off of this price.

15% of $52.50 = 0.15 × $52.50 = $7.875

Now, round to the nearest cent.    

$7.88

Finally, subtract this amount from the sale price.

$52.50 – $7.88 = $44.62

So, that sweater that was originally $75 is now only $44.62!

Sweet! Jeans at American Shmeagle are 40% off. How much will you pay for a pair of jeans that were originally $80? Don't forget the 9.25% sales tax—always calculate the discount before adding in the sales tax.

First calculate the 40% discount. We can do this by translating it into an equation:

40% (0.40) of (multiply) $80 is (equals) what (x)?

0.40 × 80 = x

Solve the equation.

x = 32

That's our discount, so subtract that from $80.

$80 – $32 = $48

That's our sale price. Now it's time to add in the sales tax: 9.25% of $48 is what?

9.25% (0.0925) of (multiply) $48 is (equals) what (x)?

0.0925 × 48 = x

Solve the equation.

x = 4.44

This is the sales tax.

Add the sales tax to the sale price.

$48 + $4.44 = $52.44

The grand total for the jeans is $52.44.

You invest $200 in a savings account that earns 4% interest each year. If you don't touch the account for three years, how much money will you have in your account after those three years?

This problem isn't quite as simple as it first seems. We need to deal with compound interest. Find the Year-End Total each year before calculating the following year's interest.

At the end of three years, your bank account now has $224.97. You've earned $24.97 just by sitting around doing nothing. Can't complain about that!

How NOT to Do It:

If you had combined the interest for the three years (4% × 3 years = 12%), then applied the interest, you would have earned less than when compounding it:

After three years your total would have been $200 + 24 = $224, a whopping 97¢ less than compound interest. 

(Yeah, that can barely buy a pack of gum, but imagine investing $200,000 instead of $200, and you can see that this really makes a difference.)

After a particularly nice lunch, your bill comes to $44.75. You and your two friends split the bill equally. How much do you each owe? (Don't forget to add in a 20% tip!)

Since we're dealing with a real-life situation, it's totally acceptable to round the amount to $45, an easy number to split in thirds.

Also, you can either calculate the tip before you split the bill, or after you split it. Either way, you'll get the same answer.