need help with percent problem

max

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Jun 1, 2007
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If a is 40% of b, then b exceeds a by what percent of a?

I think somehow the answer is 60%, but my gut tells me im wrong.

Can anyone help?

thanks
 
max said:
If a is 40% of b, then b exceeds a by what percent of a?

I think somehow the answer is 60%, but my gut tells me im wrong.

Can anyone help?

thanks

Suppose b = 100.
Then a = 40% of 100, or a = 40

Now....let's find out by how much b exceeds a:
100 - 40 = 60

What percent is 60 of 40? It isn't 60%......
 
Division is far more reliable than the gut.

a = b*40% = b*0.40 = b*(2/5)
b/a = (b/(b*(2/5))) = (1/(2/5)) = 5/2 = 2/2 + 3/2

or

(b-a)/a = [b - b*(2/5)]/(b*(2/5)) = [1 - (2/5)]/2/5 = 5/2 - 1 = 5/2 - 2/2 = 3/2

Okay, 3/2 is a lovely value. What does that make tha answer?
 
max said:
If a is 40% of b, then b exceeds a by what percent of a?
Since you've posted this to arithmetic, then you don't have the tools of algebra. So let's try to think about this in more elementary terms.

Try converting the "forty percent" to a fraction.

If "a" is forty percent of "b", then what fraction is "a" of "b"? In particular, if "b" is broken up into, say, five parts, of how many parts (of the same size) would "a" consist?

How many more parts does "b" have than does "a"?

Thinking only of this overage, what fraction of "a" is represented by the number of parts in this overage?

What percentage corresponds to this fraction?

Hope that helps a bit! :D

Eliz.
 
Thanks for the replies!

the percent of 3/2 is 150%

I am still confused in the thinking process of coming to the conclusion.

tkhunny,your solution is excellent. I understand a= (2/5)b. but I still don't understand the part starting with
b/a = (b/(b*(2/5))) what does that represent? Why is b/a? Also, why break up 5/2 = 2/2 + 3/2?

thanks
 
max said:
I am still confused in the thinking process of coming to the conclusion.
You followed through the steps provided earlier to find the solution, so you must not be entirely confused. :wink:

At which step in the process I'd provided are you having difficulty? Please be specific. Thank you! :D

Eliz.
 
Mrspi said:
max said:
If a is 40% of b, then b exceeds a by what percent of a?

I think somehow the answer is 60%, but my gut tells me im wrong.

Can anyone help?

thanks

Suppose b = 100.
Then a = 40% of 100, or a = 40

Now....let's find out by how much b exceeds a:
100 - 40 = 60

What percent is 60 of 40? It isn't 60%......

Nice!
 
Note: It is a matter of what is in the denominator.

5 is 25% greater that 4
4 is 20% less than 5

In both cases, the difference is 1, but...

1/4 = 25%
1/5 = 20%

It's an old algebra gag.

Start with 100. Add 10% of that value. Subtract 10% of that value. If you get back to 100, you did something wrong.
 
Yes Eliz, but I still don't understand why the solution was formed that way. For example, just looking at the problem I would not have seen to solve it that way but after seeing how to solve it that way I can solve it.

I'm still trying to figure why is b/a? what does that represent? I understand every step in the solving process but on a test I would not have put b/a because I don't know why it is like that.

adding 10% to a 100 =110 subtrating 10% of that amount is 99.

I think Im having a problem with translating the words too. Could you show the solution corresponding to the wording. For example, if a is 40% of b. Obviously a = .40b = 2/5b.

Also someone told me since a = 2/5b, then b = 5/2a = a + 3/2a. I have no idea how a+3/2a was formed.
 
max said:
Also someone told me since a = 2/5b, then b = 5/2a = a + 3/2a. I have no idea how a+3/2a was formed.

a = 2/5b is same as 2b / 5

a = 2b / 5 ; crisscross multiply:
2b = 5a
b = 5a / 2

5a / 2 is same as a/2 + a/2 + a/2 + a/2 + a/2 ; or a/2 * 5 = 5a / 2
Do you follow?

QUIT writing fractions like 2/5b: looks too much like 2 divided by (5*b)
 
105/100 = 1.05 = 1.00 + 0.05 = 100% + 5%

The 100% is the portion that represents where you started. <== Always!
The 5% represents the increase.

60/100 = 0.60 = 1.00 - 0.40 = 100% - 40%

The 100% is the portion that represents where you started. <== Always!
The 40% represents the decrease.

200/100 = 2.00 = 1.00 + 1.00 = 100% + 100%

The first 100% is the portion that represents where you started. <== Always!
The second 100% represents the increase.
Another way to say this one is "it doubled".
Another way to say this one is "it increased 100%".
Another way to say this one is "it increased to 200% of the original value".

1000/100 = 10.00 = 1.00 + 9.00 = 100% + 900%

The 100% is the portion that represents where you started. <== Always!
The 900% represents the increase.
Another way to say this one is "it increased to 1000% of the original value".
A common error on this one is to say it "it increased 1000%". It's just wrong, but it gets on the news and in print on occasion.

100/100 = 1.00 = 1.00 + 0.00 = 100% + 0%

The 100% is the portion that represents where you started. <== Always!
The 0% represents the increase, or the lack thereof.
Another way to say this one is "it didn't change".
 
max said:
I'm still trying to figure why is b/a? what does that represent?
That's why I gave you a solution that didn't involve algebra! :wink:

Since you're in arithmetic, and haven't yet done pre-algebra or algebra, obviously stuff done in variables and systems of equations is going to be a bit confusing. Instead, just follow the definitions (what does "percent" mean? how do fractions and percents relate? etc).

i) If "a" is 40% of "b"...: What is "forty percent" as a fraction? Given that equivalent fraction, and given the fact that "b" is 100% of "b", how many "parts" should "b" have? How many parts then should "a" have?

ii) ...then "b" exceed "a"...: How many more parts does "b" have than does "a"? What is the overage?

iii) ...by what percent of "a": Viewed in terms of "a", what fraction of "a" is represented by this overage? Into what percentage does this fraction convert?

That's all there is to it! :D

Eliz.
 
Just wanted to show I understand everything with another problem and I can solve it 2 ways!

If a is 20% of b, then b exceeds a by what percent of a?

if a is 20% of b, then a = (1/5)b then b = (5/1)a. To find how much b exceeds a would be to subtract a from b. So substitute (5/1)a for be and you get (5/1)a - a = (4/1)a. So b exceeds a by 400% of a!

or if a is 20% I could rewrite it as (20)a/(100)b then I can find how much b exceeds by subtracting and get 80 then all I have to do is find what is percent 80 is of 20 which is 400% of a :)

Thanks again Mrspi, Tkhunny, Stapelm Jonboy and Denis!!!!
 
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