Standard Questions
There are several standard types of questions involving percentages that you'll see. We'll work through one of each type here.
Example 1 – Commisions
Some types of jobs, primarily in sales, pay employees a percentage of each sale that they make. That percentage the employees get paid is called a commission.
Julia makes a 3.5% commission on all appliance sales that she makes. If she made a sale worth $135.46 what would her commission be?
Julia would get 3.5% of the $135.46 price so this is the same as asking, "What is 3.5% of $135.46." To answer that
| What | is | 3.5% | of | $135.46? |
| x | = | .035 | · | $135.46 |
| x | = | $4.74 |
Example 3 – Sales Tax
Martin buys a stereo for $225.00. If the sales tax is 6% then what's the total cost of the item?
First, we need to calculate the amount of the sales tax, i.e. we need to find 6% of $225.
| What | is | 6% | of | $225? |
| x | = | .06 | · | $225 |
| x | = | $13.50 |
At this point, we're not quite done. We've found the amount of the sales tax but the question asked for the total cost, i.e. the list price plus the tax.
| total price | = | list price | + | sales tax |
| total price | = | $225 | + | $13.50 |
| total price | = | $238.50 |
Example 2 – Percent Increase or Decrease
In 2007, the total sales for a small company were $512,552. In 2009, the sales decreased by 12%. What were 2009's sales?
This question has two parts, much like the last one. First, we need to use the percentage to find the amount by which the sales decreased then we'll subtract that amount (because sales decreased) from the starting sales amount.
| decrease | = | .12 | · | $512,552 |
| decrease | = | $61,506.24 |
Now, we can use that to find the 2009 sales amount.
| 2009 sales | = | 2007 sales | - | decrease |
| 2009 sales | = | $512,552.00 | - | $61,506.24 |
| 2009 sales | = | $451,045.76 |
Example 4 – Calculating Original Cost
Lauren paid $126.54 for office supplies. If the sales tax was 6.25%, what was the list price?
First, we need to make sure we've got out terms straight. When a question asks for the list price, it's asking for the price before the sales tax was added. Finding this amount isn't as simple as multiplying the amount paid by the percentage and subtracting, i.e. doing the same calculation you would for adding the sales tax but subtracting. The correct procedure goes like this:
Let x be the original price, i.e. the list price.
Since the sales tax was 6.25%, this means the means the sales tax would be .0625x.
Now we can set up an equation we can solve for the amount we need.
| total cost | = | list price | + | sales tax |
| $126.54 | = | x | + | .0625x |
| $126.54 | = | 1.0625x | ||
| x | = | $126.54 / 1.0625 = $119.10 | ||
