Math Question

[theantiquetiger]

I am at work and in a discussion with some one about something we heard on the radio.

The ad said "increase your reading speed 1000%", "read 10 books in the time it takes you to read 1 book now".

My fellow employee says this is wrong, by his math, you will be reading 11 books if you increase your speed 1000%, I say 10 books.

Another example we are using is profit. He says if I spend $100 on something and sell it for $150, I have a 50% profit, I say 150% profit.

The final example we are using are apples. If he has an apple, and he increases his apple supply 100%, he says he now has 2 apples, I say he didn't increase.

What do you think?

[Hulk]

Scenario A (1000 percent increase)

If you increase 100 percent, you can read two books in the time you can read 1. Increase 200 percent, you three books, in the time you can read 1, etc. Your employee is right (at least in my book).

Scenario B ($50 profit):

You have 100 dollars. You buy something for $100. You sell it for $150. You have $50 more than you did before which is the definition of profit, therefore you have a 50% profit (50 is 50 percent of $100).

Scenario C (100 percent increase):

100% of 1 is 1. If you increase (add) 100 percent to your supply, you have double your original supply. You have two apples.

[imp]

I am at work and in a discussion with some one about something we heard on the radio.

The ad said "increase your reading speed 1000%", "read 10 books in the time it takes you to read 1 book now".

My fellow employee says this is wrong, by his math, you will be reading 11 books if you increase your speed 1000%, I say 10 books.

Another example we are using is profit. He says if I spend $100 on something and sell it for $150, I have a 50% profit, I say 150% profit.

The final example we are using are apples. If he has an apple, and he increases his apple supply 100%, he says he now has 2 apples, I say he didn't increase.

What do you think?

I say…

Your co-worker is absolutely correct and you are absolutely wrong?

I understand the "%" sign to signify "per cent," (or "per 100 units") which suggests a percentage of the original quantity or volume.

In your first example (books), "1000%" of "1 book" (or, 1,000 divided by 100 [per cent]) would be 10 books, and I suspect your co-worker includes the original, 'read' book as the 11th book.

In your second example (profit), the "50% profit" is contingent upon the word "profit." You have to remember, in your analogy, your principal cost was $100. But you only earned HALF that amount by selling it. Therefore, your profit is HALF of the original principal… $50. In other words, your PROFIT is 50%, or $50.

In your final example (apples), I think your co-worker is correct once again. Remember, 100% of "1" apple is … (say it with me, now)… "1 apple." If the apple-collector in your analogy increases his apple count by "100%," he has effectively added one apple. If he already had one apple, he now has two apples.

Benjamin

[theantiquetiger]

Scenario A (1000 percent increase)

If you increase 100 percent,

I see 100% increase as no increase. 200% increase is double. I read increase as a change in value, so 100% is the same as the first value.

Another scenario we are discussing is if runner A is 100% faster than runner B, than A is 2x faster than B. Using that same logic, if A is 200% faster than B, he is 4x faster than B. My fellow employee says if A is 100% faster, he is 2X faster.

Hulk, you are an accountant (or something along those lines, correct?), we need some scientific mathmaticians.

My friend says "increase" only means to go up, I see it as a change in value (up or down), making 100% the same value as the original value.

[imp]

I see 100% increase as no increase. 200% increase is double.

This might be where you're getting tripped up. As discussed in my earlier post, a 'percentage,' or '%' relates to the ORIGINAL quantity or volume. If you agree that "100%" equals "1," then we're in good shape.

But you can't exclude the original quantity or volume!

I read increase as a change in value, so 100% is the same as the first value.

NOT the same. It's the full percentage value PLUS the original value!

Another scenario we are discussing is if runner A is 100% faster than runner B, than A is 2x faster than B. Using that same logic, if A is 200% faster than B, he is 4x faster than B. My fellow employee says if A is 100% faster, he is 2X faster.

Exactly. Because, as discussed above, the final value is the full percentage value PLUS the original value.

My friend says "increase" only means to go up, I see it as a change in value (up or down), making 100% the same value as the original value.

Perhaps it would be easier to comprehend if your friend stated that a "percentage increase" meant adding the "percentage" value TO the original value.

It's tricky stuff, and I'm no mathematician. I'm just trying to lay it out in simple terms, the way I best understand it.

Benjamin

[theantiquetiger]

I actually see it both ways, but I think "mathmatically", the way I am talking about is correct, even though everyone (including me) use it the way my fellow employee sees it.

[Adam West]

I am at work and in a discussion with some one about something we heard on the radio.

The ad said "increase your reading speed 1000%", "read 10 books in the time it takes you to read 1 book now".

My fellow employee says this is wrong, by his math, you will be reading 11 books if you increase your speed 1000%, I say 10 books.

Another example we are using is profit. He says if I spend $100 on something and sell it for $150, I have a 50% profit, I say 150% profit.

The final example we are using are apples. If he has an apple, and he increases his apple supply 100%, he says he now has 2 apples, I say he didn't increase.

What do you think?

I skimmed through most of the responses and I think everyone is generally correct so I apologize if I am restating what was already answered.

Scenario 1- The key in 1000% is it 10 additional books to the one or not?
If it is 10 books total the increase is 900% 10 books -1 book = 9/1=900% but if it is 11 total than it is 11-1=10/1=1,000%

Scenario 2-Profit equals the money above and beyond your cost. In this case your Income was $150 and your cost was $100. To calculate profit, it's
revenue-cost/cost so $150-100/$100 which =50% profit

Scenerio 3-start with 1 apple and end with 2. Same formula as above 2-1/1
=100% increase in apples.

[Adam West]

I see 100% increase as no increase. 200% increase is double. I read increase as a change in value, so 100% is the same as the first value.

Another scenario we are discussing is if runner A is 100% faster than runner B, than A is 2x faster than B. Using that same logic, if A is 200% faster than B, he is 4x faster than B. My fellow employee says if A is 100% faster, he is 2X faster.

Hulk, you are an accountant (or something along those lines, correct?), we need some scientific mathmaticians.

My friend says "increase" only means to go up, I see it as a change in value (up or down), making 100% the same value as the original value.

Maybe this will help. Let's say you make $40,000 and get a 5% increase. Your new salary would be $42,000 right? Now let's say all you know is I was making $40, now I'm making $42, what is my % increase. Using the exact same formula $42,000-$40,0000=$2,000. $2,000/$40,000 = 5%

So if you are seeing 100% as being the same, that's incorrect. Use the example above. Your making $40,000 and get a 100% increase. Is your new salary still $40,000?

For the runner scenario, it might be easier to apply real numbers.

Runner A can run a 400M race in 2 minutes. Runner B can run a 400M race in 1 minute. Runner B is twice as fast as Runner A. Runner B has crossed the finish line while Runner A is only halfway around the track.

To be 4 times as fast, this is just basic algebra. 4x=2 minutes (or 120 seconds). 120/4=30 seconds which is 4 times faster than Runner A.

[JPkempo]

You are both correct % of total % of original.
Ads use what ever math is in there favor. If a drink has 2 cups of fluid in it (now 3 cups). The new total is 33.3% of the total or 50% more or 150% of the original.

So in your ad it dosn't say from original amout or including the original amount. Face it round number sound better, so thats what they used. So in the 3 % math senarios the numbers could be 9, 10, or 11. Althou 11 is more 10 sounds better.

[theantiquetiger]

I was just trying to look at it in true "math terminology". I don't think there is a true defined meaning in math for "increase", I think the math world only sees "increase" as a change in value, since you could increase a value with a negative number, which would actually decrease the value.

Thats is way I was wondering if there is a math teacher, professor, or some other kind math expert here.

[Adam West]

I don't claim to be a math expert, but I have two undergraduate degrees, one in Finance and one in Accounting and am a CPA. As far as math, I have taken linear regression classes which was the class after Calculus 2.

Increase in math terms can be expressed in $ or %. In the examples you gave, they were expressed in % and to calculate a % increase your numerator is the absolute value of the increase minus the base line value. The denominator is the baseline value. So mathematically to get to a 1000% increase 11 books have to be read 11-1=10/1 which is 1000%.

The only way you can have a % increase with negative numbers is if the baseline value has a higher negative value than the increase so moving from ($50) to ($10) is a % increase.

If your starting point is 0, you can not calculate a % increase because a number can't be divided by 0.

[Hulk]

So I guess everyone else in this thread, and your friend, are still wrong, and a scientific mathematician will somehow proof your point?

I know of no special mathematic value attributed to the word increase other than its common definition to grow, augment, make larger, etc (all implying the addition or multiplication of a positive value).

PS - I am by no means a mathemetician or accountant, but if I thought of profit in the same way you did, and told the IRS, they'd tax me so hard I wouldn't have a profit. Think about that when you are reporting profit from your garage sales business to them.

[theantiquetiger]

So I guess everyone else in this thread, and your friend, are still wrong, and a scientific mathematician will somehow proof your point?

No, I agree with everyone here, I am just wondering if we are correct. When it is 2am in the morning, and there is nothing going on at work, we have some really strange discussions!!

PS - I am by no means a mathemetician or accountant, but if I thought of profit in the same way you did, and told the IRS, they'd tax me so hard I wouldn't have a profit. Think about that when you are reporting profit from your garage sales business to them.

My fellow emploee said almost the exact same thing!!