When I was in high school, I weighed 125 pounds fully clothed and soaking wet. I couldn’t do anything to change it, either. That was the worst part. I yearned to play varsity baseball, but at my weight, I just straight up wasn’t big enough.

College was mostly the same, although I filled out a little. I’d say my average weight in college reflected the “freshman 15,” but for me it was a welcome change.

Then I got a job, spent 4 years sitting on my ass all day, eating large fast food meals, and not getting any exercise. I weigh about 170 now.

So over the years, I’ve put on 45 pounds. Damn. What’s the percent change in my weight from high school to now?

Here’s the general formula for this kind of question:

So plug my values in:

And would you look at that? The percent change in my weight is 36%. Holy balls. I need to go on a diet.

So now say I go on some crazy workout plan, and I lose 45 pounds, so I’m right back where I started at 125. What will be my percent change then? Note: if the answer was just going to be 36% again I probably wouldn’t be wasting your time with this.

Whoa. So it was a 36% gain, but now it’s only about a 26.5% loss? How is that fair? A sorta strange truth about percents (this is true about ratios, too) is that the bigger the numbers are, the less difference a difference makes.

If you’re 16 and your little brother is 13, you’re about 123% his age. But when you were 4 and he was 1, you were 400% his age. The older you both get, the smaller the percent difference will be, but you’ll always be 3 years older than him.

This is also why it’s socially acceptable if your dad is 10 years older than your mom, but it would have been pretty creepy if they met when he was 26 and your mom was 16.

Example Questions:

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Comments (23)

hey!!!!!!Can u SOLVE this Question—The price of a telephone was first increased by 10% and new price was decreased by 25%.The final price was what percent of the initial price????

Plug in 100 for the original price of the phone. That way, when it goes up 10%, it becomes 110. 25% of 110 is 27.5, so when it goes down 25% it will become 110-27.5=82.5.

The nice part about plugging in 100 for questions like this is that when it’s over, you just have to ask yourself what percent of 100 is 82.5? 82.5%, of course!

A store charges $28 for a certain type of sweater.This price is 40% more than the amount it costs the store to buy one of these sweaters.At the end of the season sale,store employee can purchase any reamaining sweaters at 30% off the stores cost.How much wud it cost an empoyee to purchase s sweater of this type at this sale??

Wait, is this kind of like the age example that you mentioned earlier? Since the numbers are bigger the percent change becomes smaller?

Sure. An increase of 25% can be written a bunch of different ways, depending on how you prefer to deal with percentages. Personally, I like to do it this way:

25% of $75 is:
(25/100) × $75 = $18.75

So her hourly wages increased by $18.75. Since she was making $75 before, now she makes $93.75 per hour. That’s better than she was doing before, but still not as good as Steve, who makes $100.

Her wages are now what percent of Steve’s?

93.75 is what percent of 100?
93.75 = (x/100) × 100
93.75 = x

So, unsurprisingly, 93.75 is 93.75% of 100.

First, you have to figure out the amount of change that happens from month to month:

From March to April: $400
From April to May: $600
From May to June: $500
From June to July: $800
From July to August: $700

Then you apply the percent change formula in this post. For each answer choice, you can calculate the percent change based on how much change occurred, and what the starting value was.

From March to April: $400/2000 = 0.2
From April to May: $600/2400 = 0.25
From May to June: $500/3000 = 0.1667
From June to July: $800/3500 = 0.2286
From July to August: $700/4300 = 0.1628

So the biggest percent change happens from April to May.

There’s a backsolved solution worked out here.

If you’re looking to do it algebraically, you’re going to have to write a few equations:

m + n = 120
(we know this because they both end up with 60 in the end whcih means they always had a total of 120 marbles.)

2(m – 60)/m = (60 – n)/n
(this is the algebraic representation of “change/original” that will give positive values for “change” for both people, with a 2 in front of Arnold’s to represent that his loss was half of Sophie’s gain)

Solve that system, and you’ll find that m = 80.

(Of course, since you know Arnold didn’t give Sophie zero marbles, the only answer is m = 80.)

If you ask me, backsolve is a little easier. 🙂

Oh, umm like when you divided 60-120-m by 120-m and got 60/120-m) -1. How did you get the number? I thought 120-m would cancel with each other. Sorry if I’m confusing!!

Ah…OK. Break that into 2 steps:

(60 – (120 – m))/(120 – m)
= 60/(120 – m) – (120 – m)/(120 – m)
= 60/(120 – m) – 1

Does that make it more clear? It’s just a more complicated version of this:

(x – y)/y
= x/y – y/y
= x/y – 1

percent = amount of change / original

For #11 I know the answer, but I don’t know how to get it using this formula provided.

25% of 75 is 18.75. So 18.75 is the change in wage. Therefor I put 18.75/75 and get .25. If I multiply that by 100 then I get 100. Where am I going wrong with this?


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