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 .

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

Now cross multiply.

And divide by the coefficient (100).

So, you earned $50 in commission.

Combining your commission and wages, you earned a total of
 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 have been wanting for the past year. It was $220 before the sale. How much is it now?

Nice find! Ok, 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:

65% (0.65) of (multiply) is (equals) what (x)?

Now, solve the equation.

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.

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.

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

cross-multiply and divide   

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

Now we need to take 15% off of this price.

15% of $52.50   

Cross-multiply and divide.

Now, round to the nearest cent.     

Finally, subtract this amount from the sales price.

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

How NOT to solve it:

If you had combined the discounts and taken 45% off the original price, the sweater would have cost:

What a steal. Bummer it doesn't work that way.

Sales tax in the state of California is 9.25%. After shopping at a Shmarget in Laguna Beach, your purchases came to $62.75, before tax. How much do you end up paying, including tax?

Add the 9.25% sales tax. In order to do that, find 9.25% of $62.75. 

Here it is set up as a proportion.   

Now, cross-multiply and divide.

This is the sales tax.

Finally, add the sales tax to the total.

$5.80 + $62.75 = $68.55

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

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)

Look Out: always calculate the discount before adding in the sales tax

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

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

Solve the equation.

And subtract that from $80.

Now it is time to add in the sales tax: 9.25% of $48 is what?

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

Solve the equation.

This is the sales tax.

Add the sales tax to the sale price.

The grand total for the jeans is: $52.44

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

This problem is not as simple as it first seems. We have 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 have 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 are 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.