Need help with this GMAT Quant question?

Question

Beth, Naomi, and Juan raised a total of $55 for charity. Naomi raised $5 less than Juan, and Juan raised twice as much as Beth. How much did Beth raise?

A.  $9
 B. $10
 C. $12
 D. $13
 E. $15

Shruti T · Accepted Answer

You can just set up some quick variables. Say Beth raised B dollars. Juan raised twice that, so J = 2B. Naomi raised $5 less than Juan, so N = 2B &ndash; 5.
Now total is: B + (2B &ndash; 5) + 2B = 55 That&rsquo;s 5B &ndash; 5 = 55 &rarr; 5B = 60 &rarr; B = 12
So Beth raised $12. No need to overthink it. Answer is C.

V Gupta · Answer

Let Beth = B, Naomi = N, Juan = J. We know three things:

B + N + J = 55
N = J &ndash; 5
J = 2B

Plug #3 into #2 &rarr; N = 2B &ndash; 5 Now plug both into the total: B + (2B &ndash; 5) + 2B = 55 Simplify: 5B &ndash; 5 = 55 &rarr; 5B = 60 &rarr; B = 12
So Beth raised $12 Answer is C