Percent Off, Increase, Decrease

Percent Off

We frequently face situations in which items are on sale and the sale price is described as x% off. This type of problem may be solved as either a two step or a one step computation.

Example: We desire to buy a TV that has a list price of $600, but is on sale for 30% off.

 Two steps: First we compute 30% of 600 which tells us how much we will save by buying the TV on sale.

0.30($600) = $180.     This is the amount saved.

Then the amount we actually pay (before tax) would be $600 – $180 = $420. The sale price of the TV is $420.

In order to solve the problem in one step, we note that the list price is 100% of the list price and the list price is being reduced by 30% of the list price. Therefore, we would pay 70% of the list price, since (100% – 30%) = 70%. So if all we are interested in is the sale price of the TV, we can compute 70% of $600.

One step: 70% of $600 which is 0.7($600) = $420.

The sale price of the TV is $420.

Self Check Problem

A MD Hardware is holding a "Bag Sale" where a person will get 40% off on the price of all items that the person puts in the bag. The total value of all items in Pat's bag is $397. How much does Pat have to pay?

Solution

Reduced by, Decreased by, % Discount

Reduced by 20%, Decreased by 20%, and Received a 20% Discount all mean the same as 20% off. In any of these cases, we still have a choice of working the problem in one step or in two steps.  

Example: In order for everyone at the company to keep their jobs during the recession, each person's salary is reduced by 20%. To figure out what a salary would be after this pay cut, we would find 20% of the current salary, and then subtract the result from the current salary. Or we could also just compute 80% of the current salary, since 100% – 20% = 80%.

Two steps: For a current salary of $30,000 that is to be reduced by 20%, we find the amount of pay cut by finding the amount the salary is reduced by and then subtracting the result from the current salary.

The amount being cut is 20% of $30,000, which is 0.2($30,000) = $6,000.

So the reduced salary is $30,000 – $6,000 = $24,000.

One step: We may also find the reduced salary in a single step. Since 100% – 20% = 80%, this means that your reduced salary will be 80% of your current salary.

So your reduced salary is 80% of $30,000, which is 0.8($30,000) = $24,000.

Self Check Problem

A DevMart has advertised that the price of all items in the store are being reduced by 15%. Lynn has a DevMart coupon for a 10% discount on on any item purchased. If Lynn is allowed to have both the price reduction and to use the coupon, what percent decrease in price would Lynn get on any purchased item?

Solution

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