Question: Students at ABC Academy

Comment on Students at ABC Academy

After you get G, why not plug that into G-20? Why go back to the original ratio?
greenlight-admin's picture

Once we know that G = 60, we find the value of B by plugging G = 60 into an equation that relates both G and B. The equation 3G = 5B is such an equation.

To answer your specific question, we need to consider what G - 20 is. First off, it isn't even an equation; it's an algebraic expression that represents the number of girls remaining AFTER 20 girls leave. So, plugging G = 60 into that expression will just tell us that there are 40 girls remaining after 20 girls leave. This will not (directly) tell us the value of B (number of boys).

Hello, I am loving your content!

I did it like this:
(5x-20/3x-20) = 5/2; solve for x; x = 12
the answer will be 8x = 96
greenlight-admin's picture

Perfect solution!!

I started trying to do this approach when I first got to this question but got lost along the way. I get most of it now but I'm still struggling to understand where 8x comes from. Is it from adding the terms in the ratio 5:3?
greenlight-admin's picture

I'm not a big fan of the approach of representing the boys and girls with 5x and 3x.
I feel there are a couple of potential pitfall that may occur on test day.

Here's the rationale that people use when applying this technique:
If we say 5x = number of boys
And say 3x = number of girls

Then the ratio of boys to girls = 5x/3x = 5/3

We get: (5x-20))/(3x-20) = 5/2
Solve for x to get: x = 12

The question ask us for the TOTAL number of children.
Since 5x = number of boys, and 3x = number of girls, the total number of children = 5x + 3x = 8x
So, we must evaluate 8x for x = 12
We get: 8(12) = 96

Does that help?

Cheers, Brent

im confused on how you get G = 60 from 2G + 60 = 3G ?
greenlight-admin's picture

Start with: 2G + 60 = 3G
Subtract 2G from both sides to get: 60 = 1G
In other words, G = 60

More on solving equations here:


Great, thank you!

How do you know that they are looking for the amount of students AFTER 20G and 20B leave instead of before?
greenlight-admin's picture

It all comes down to verb tense.

The first sentence tells us that the ratio IS (present tense) 5 : 3, which means this is the PRESENT ratio.

The second sentence, with IF and WERE, tells us about a HYPOTHETICAL scenario that COULD happen, which would change the ratio of students.

The last sentence asks, "How many children ATTEND (present tense) ABC school?"
So, the question is asking for the CURRENT (present) number of students. That is, we want to determine the number of students BEFORE any hypothetical changes occurred.

Does that help?


My approach was different.
Since we know the number students who attended ABC academy must be some multiple of (5+3=8), and then the remaining students after 20 girls and 20 boys had left will be some
multiple of ( 2+5=7). You'll realize its only the 96 that meets those conditions
greenlight-admin's picture

Perfect approach - great work!!!

I just wanted to know if my reasoning and approach are correct for this solution. I started off by making the equation:

2x + 5x = x - 40 (this was pertaining to to the statement that 20 boys and 20 girls were to leave the school, along with the corresponding ratio of 2:5)

after solving for x i got 8, which i plugged back into each corresponding value to get 2(8)= 16 and 5(8)=40 that added up to 56, then i added the 40 back to the number of students that left to get 96.
greenlight-admin's picture

It's hard for me to tell whether that solution is valid.
What does x represent?
Also, can you explain the steps you took to get the equation 2x + 5x = x - 40?

I have an interesting solution to the question. Please let me know if that's correct.
Initially, the ratio is 5:3 and after subtracting 20 boys and girls, the ratio becomes 2:5.
Let x be the total number of students, so x-40 will be the number of students later (20 boys and 20 girls).
Since the number of students can't be fractions, x-40 should be divided by 7 (as the ratio is 2:5).

The only option E satisfies this condition. 96-40 = 56 which is divisible by 7.
greenlight-admin's picture

Perfect reasoning!! Nice work!!

Thanks Brent. :)

In this question once we get x =12 we would just plug it back into 5x and 3x to get the total number of students If it had asked for the current number of students would we then plug it into 5x-20 and 3x-20?
greenlight-admin's picture

All of that is correct, Ravin.

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