# Lesson: Combining Ratios

## Comment on Combining Ratios

### HI ADMIN, CAN U PLS EXPLAIN

HI ADMIN, CAN U PLS EXPLAIN ME BELOW QUE.

THE RATIO OF PENCILS' NUMBER TO THE PENS' NUMBER IS 5 TO 3. IF THE PENS' NUMBER EXCEEDS 2/5 THE PENCILS' NUMBER BY 4 , WHAT IS PENS' NUMBER? ### You bet!

You bet!

Let C = # of pencils
Let N = # of pens

"THE RATIO OF PENCILS' NUMBER TO THE PENS' NUMBER IS 5 TO 3"
So, C/N = 5/3
Cross multiply to get: 3C = 5N

"THE PENS' NUMBER EXCEEDS 2/5 THE PENCILS' NUMBER BY 4"
N = (2/5)C + 4
Multiply both sides by 5 to get: 5N = 2C + 20

We now have two equations:
3C = 5N
5N = 2C + 20

Since both equations are set equal to 5N, we can write: 3C = 2C + 20
Solve to get: C = 20
If C = 20, then N = 12

So, there are 12 pens and 20 pencils

### Got You. I often confuse with

Got You. I often confuse with the terms framed in the que. Anyways thanks for the help. I understood now.

### just to add something =)

we could also simplify 24/T=3/4 --> 8/T = 1/4

may help with more hairy problems =) ### Looks good to me!

Looks good to me!

### Hi Brent! Could you please

Hi Brent! Could you please provide a solution to this question, I do not seem to understand how to work through it. Thanks!

https://gmatclub.com/forum/the-ratio-by-volume-of-soap-to-alcohol-to-water-in-a-68933.html ### We can do this right?

We can do this right?
P/B*B/T= 5/2*3/4
P/T=15/8
P=60
T=8/15*60=32 ### That's a perfectly valid

That's a perfectly valid solution. Nice work!

Cheers,
Brent

### https://gmatclub.com/forum

https://gmatclub.com/forum/the-ratio-by-volume-of-soap-to-alcohol-to-water-in-a-68933.html

Hi Brent , for the above question I didn’t understand the part where we have to double and halve the ratios. When I did it I doubled both the ratio terms to have 4/100 (after doubling ) and 1/50 after havle . Can you please explain me this part, why are we only changing one term Tricky question!!
Doubling both ratio terms won't double the ratio (we're told that "the ratio of soap to alcohol is doubled")
Initially, the ratio soap/alcohol = 2/50
So, doubling the ratio means the ratio soap/alcohol = 4/50
Notice that 4/50 = 2(2/2/50). That is, the ratio 4/50 is twice the ratio 2/50

In your solution you doubled both ratio terms to get 4/100. However 4/100 and 2/50 are equivalent ratios. So the ratio hasn't been doubled.

Does that help?

### Oh now i get it..if I double

Oh now i get it..if I double both the terms I will get equivalent ration , not the double..it makes sense now.. I will have to be more careful with this.

Thanks Brent!!!

### https://gmatclub.com/forum/on

https://gmatclub.com/forum/on-a-certain-sight-seeing-tour-the-ratio-of-the-number-of-women-to-th-68645.html

My thinking could possibly be wrong,

So I do get the correct solution but, I was thinking that, since 5+11 is 16, the number (which is less than 30) must divide to an integer, so only 16 would work 