# 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