After a 20% reduction, you purchase a new suit for $276. to find the original price of the suit.

Question

After a 20% reduction, you purchase a new suit for $276. What was the price of the suit before the reduction?

A) First write an equation you can use to answer this question. Use x as your variable and express any percents in decimal form in the equation.

The equation is

B) Solve your equation in part [A] to find the original price of the suit.

Answer: The original price of the suit was dollars.

Answer 1

Treena, if there was a 20% discount, then you paid 80% of the original price. Since we don't know the orginal price, we will assign it the variable x. Change 80% to a decimal. The equation would be:

.8x = 276   To get the variable by itself, divide each side by .8.

.8x/.8 = 276/.8

x = 345

The original price of the suit was $345.

Hope this is helpful.

Answer 2

The Always Works approach for percent problems like these is to set it up as a fraction problem:

percentage / 100 = part / whole

For any problem, you'll know two of these, and have to find the last.  In this case you know the partial price of the suit - that is, you know the price that is just a part of the full price.  That's your "part".  You also know the percentage it is - it's a 20% discount, so you paid 80% of the full price.  That's your "percentage".  What you want to know is the full price, that's the "whole".  Now you can set it up like this:

80 / 100 = 276 / x

Now it's just a fraction problem!  Using this set up will help you with a LOT of percentage problems, and I really recommend it!

 

So, that's how you set it up, and if you know how to solve it from there then you can stop reading now.  However, I know many students panic in the face of fractions, so let me walk you through how to actually solve for x:

80 / 100 = 276 / x

What you're going to do is called cross multiplication, and a lot of students remember it as "the butterfly thing" : D  You're going to multiply the bottom of each fraction by the top of the fraction on the other side:

80x = 276 * 100

80x = 27600

Now it's just a matter of getting the 80 off the x!  The 80 is being multiplied by the x, so to get it off we use division:

80x/80 = 27600 / 80

x = 27600/80

Grab a calculator and see that 27600/80 = 345, so we have:

x = 345

That's the full price of the suit, so your final answer is $345!