Problem Solving

Hi there,

I'm new to the Beat the GMAT community and I'm so psyched I found this place! Already, everyone has been so helpful. I need some help with this problem. I'm not sure if there's a typo in my book, or if i just am not getting this -- this is a fairly simple ratio question.

If cement, gravel, and sand are to be mixed in the ratio of 3:5:7 respectively, and 5 tons of cement are available, how many tons of the mixture can be made?

a) 15
b) 20
c) 25
d) 30
e) 75

answer: C

Here's the book's explanation
Since the ratio of cement to gravel to sand is 3:5:7, for every 3 portions of cement we put in, we get 3+5+7 or 15 portions of mixture. Therefore the recipes gives us 15/3 or 5 times as much mixture as cement. We have 5 tons of cement available, so we can make 5x5 or 25 tons of the mixture.

This is in the Kaplan Math Workbook.

The explanation seems fairly straightforward, maybe your mind is blocked and you are too tired to see what they're trying to explain - this has happened to me on numerous occasions.

I'll show another, slightly more tedious way of solving the problem. Hopefully it'll help:

ratio -> 3:5:7

we have 5 of cement, to get this in the ratio, we have to multiply 3 by (5/3) since 3*5/3 = 5

so now that we have 5 for cement, we have to multiply the other units in the ratio with the same value (5/3)

-> gravel = 5*(5/3) = 25/3
and sand = 7*(5/3) = 35/3

Adding all the 3, we have 5 + 25/3 + 35/3 = 5 + 60/3 = 5 + 20 = 25

Please let me know if you're still having problems with this.

oh my goodness... ha! yes, i see it. i was just blocked. I was "looking" for something else. (Plus, there was a typo earlier in the book that had me working on a problem for way too long, and now I'm paranoid there are going to be more.) Thanks so much!