A SAT question

[belly_ttt]

I know this is not a mathematics forum but since the exam is somewhat linked to the English language I'm going to ask this question:
From 1985->1990, the berry production of bush xx increased by 20%. From 1990->95, the berry production increased by 30. What was the percent increase in the berry production on the bush over the entire 10-year period from 85-95?

Do the question without using the number substitution skill or anything, just use the arithmetic way


Here was my take:
20+20*30%=26%.

But the answer turned out to be wrong. What was wrong with it? And what is the correct answer? (Please do it slowly and explain it carefully in case I'm lost)
Thanks in advance

[Raymott]

I know this is not a mathematics forum but since the exam is somewhat linked to the English language I'm gonna (going to)! ask this question:
From 1985->1990, the berry production of bush xx increased by 20%. From 1990->95, the berry production increased by 30. What was the percent increase in the berry production on the bush over the entire 10-year period from 85-95?

Do the question without using the number substitution skill or anything, just use the arithmetic way

Here was my take:
20+20*30%=26%.

But the answer turned out to be wrong. What was wrong with it? And what is the correct answer? (Please do it slowly and explain it carefully in case I'm lost)
Thanks in advance

You're right: it's not a maths forum, so I felt obliged to correct your "gonna"
To the question:
Give the original berry production an index of 100. An increase of 20% gives 120.
An increase of 30% from 120 gives 136. So the overall increase is 36%.

[belly_ttt]

Hi Raymott,
I forgot to add this. The result is 56, not 36. And I don't know why.
By the way, I think I've just mentioned not to use any number substitute skill, I just want to get the result the arithmetic way

[Raymott]

Hi Raymott,
I forgot to add this. The result is 56, not 36. And I don't know why.
By the way, I think I've just mentioned not to use any number substitution skill, I just want to get the result the arithmetic way

Oops, sorry. Yes the answer is 56.
100 -> 120 -> 156. (Last time I added 36 to 100 instead of to 120)

Well, you don't have to use an index. That was just to explain it to you. You could do it in your head. I don't know what you mean by the "arithmatic way"
Maybe :
Let the original production be x;
At 1990, the production is x + x * 20/100 = 1.2x
At 1995, the production is 1.2x + 1.2x * 30/100 = 1.2x + 0.36x = 1.56x
This is an increase of 0.56x, or 56%.

[belly_ttt]

I mean, we don't pretend any number as the original. Can we just do the multiplication or adding and subtracting?
And by the way, could you check out my original result. Because I don't know where I went wrong

[Raymott]

I mean, we don't pretend any number as the original. Can we just do the multiplication or adding and subtracting?
And by the way, could you check out my original result. Because I don't know where I went wrong

Using x, a variable is exactly what mathematicians do when they don't want to use an initial number. No you can't multiple something if it doesn't exist. However there is one solution. Change the variable x back to "berry production" in my previous working.

Your original
Here was my take:
20+20*30%=26%.
By using 20 for the result of the first calculation, you are taking an index of 100, since 20% of 100 is 20. However, the problem (where you went wrong) is that for the second calculation, you are applying the 30% increase only to 20, not the total 120 that you have so far.
120 + 120*30% = 156, a 56% increase.

[belly_ttt]

So I continue to wonder, where does the 100% come from?

[Raymott]

So I continue to wonder, where does the 100% come from?

It comes from the original berry production, which is where you start.
The original berry production = 100% of the original berry production.
If there's a 20% increase over the original berry production, you have 120% of the original berry production, not 20% (which would be a decrease).

[belly_ttt]

So what if we pretend the berry procution to be a 0 and rise to 20%?
- Ah, that's would be impossible because 20% of 0 is still 0.
Thanks Raymott, all clear

[Raymott]

So what if we pretend the berry procution to be a 0 and rise to 20%?
- Ah, that's would be impossible because 20% of 0 is still 0.
Thanks Raymott, all clear

Phew, well as long as you understand it now, I guess it was worth while!