## Strategies in Solving Discount Problems

In the previous post, we have learned how to solve discount problems. In this post, I am going to teach you some strategies that will make solving faster. We know the Civil Service Examinations, as well as other examinations, are always under time pressure. Being able to solve problems fast will be a great advantage.

We are going to solve the same problems, only this time, we are going to use strategies that would be able to make solving discount problems faster. You are probably wondering why I didn’t teach this strategy the first time. The answer is, you have to know the basics first, so if you forgot your strategy or shortcut, you can always go back to the long method.

Sample Problem 1

A movie DVD which costs 600 is marked “25% off.” What is the discount? What is its sale price?

Discussion

In the previous post, we used decimals to solve this problem. However, percentages like 25%, 50%, 75%, 10%, 75% and the like are easy to convert to fractions. If you are familiar with their equivalent fractions, it is easier to solve the problem above.

Solution

The equivalent of 25% is 1/4 and 1/4 is half of half. So, half of 600 is 300 and half of 300 is 150. Therefore, the discount is P150 and the sale price is P600-150 = Php450.

You see, you can solve the problem above mentally.

Sample Problem 2

Anna shops in an international store. A t-shirt with a tag price $42 is marked “save 20%.” How much will Anna have to pay for the t-shirt if she were to buy it? Discussion In the previous post, we multiplied$42 by 0.2 (or 20%), then subtract the result from 42. Note that if you subtract the percentage first, the calculation will be easier. That is, if the discount is 20%, then, we only have 20 pay 80%. Therefore, we just have to multiply  0.8 by 42.

Solution

The discount is 20% so we only need to pay 80% of the $42. So, (42)(0.8) = 33.60. This means that the sale price is$33.60.

Sample Problem 3

After getting a 10% discount, Nina bought a sofa for only 7200. What was the original price of the sofa?

Discussion

Again, like in Problem 1, it is faster to convert 10% to fraction. The discount is 1/10, so this means that Nina only paid 9/10 of the original price. So, we can set  up the equation $\frac{9}{10}x = 7200$.

Solution

The discount of the sofa was 1/10, therefore, Nica paid 9/10 of the price which is 7200. Setting up the equation, we have

$\frac{9}{10}x = 7200$

$9x = 72000$

$x = 8000$

So, the sofa cost Php8000.00

That’s it. In the next post, I will post some sample problems discount problems for your practice.