TJ B. answered • 06/28/19

Harvard Tutor in Mid-Wilshire

Hi Nausheen,

Here, there are three key things to remember.

One, that percent changes should be dealt with separately and not added or subtracted. For example, if I marked a $100 shirt up 50% to $150, but then marked that down by 50%, what would I get? Not $100. No I would get $75, which is half of $150. Notice that each time you're making a percent change on a cost, you're taking a percent of a different number, meaning we have to take this one step at a time.

Two, that percent as a decimal times whole equals part. For example, a tip of 20% on a $100 meal would be .2*100= $20. That you probably know, but it's useful to remember and think, which parts of this equation do I have? What don't I know?

Three, that percent change is the difference divided by the original amount. For example, if a $100 shirt now costs $148, the difference $48/ original $100 gives us that this shirt is marked up 48%.

Here - we don't have an original cost for the article. We can do two things as a result– either make up a number, or use algebra.

MAKE UP A NUMBER: Imagine the article first cost $100. This is an easy number to choose for percents, as we've seen. What is that marked up by 20%? Well .2*100=20, plus $100 is $120. Easy. Now the shopkeeper discounts that by 12%. So we do .12*120, and get that the shopkeeper took $14.40 off the shirt. It's now worth $105.6. What is the gained or lost percentage? Well first it's a gain, since it's higher than the original $100. Second, we can use the percent change equation, difference/original. Here, that's 5.6/100, or a 5.6% increase.

ALEGBRA: Using algebra we can do the same thing. Let's say the article cost is $x. The new cost would be .2x+x, or, if we factor out the x to make this x(1+.2), that's 1.2*x. Then we mark that down by .12, so 1.2x – 1.2x(.12), or 1.2x(1-.12) or (1.2)(.88)x which equals 1.056x. That multiplication represents a 5.6% increase in x, the original cost of the article.

Let me know if you have any questions Nausheen! I hope that helped explain it!