Question 174709: one number is 16 more than another. If the smaller number is subtracted from two thirds of the larger number, the result is one fourth of the sun of the two numbers. Find the numbers.
Found 2 solutions by Mathtut, Edwin McCravy:
Answer by Mathtut(3670)   (Show Source):
You can put this solution on YOUR website! lets call the smaller and larger numbers, S and L , respectively
:
L=S+16........eq 1
1/4(L+S)=(2/3)L-S..eq 2
:
take L's value of S+16 from eq 1 and plug it into eq 2
:
1/4(S+16+S)=(2/3)(S+16)-S.....multiply all terms by 12
:
3(2S+16)=8(S+16)-12S
:
6S+48=8S+128-12S
:
10S=80
:
:
Answer by Edwin McCravy(20059)  (Show Source):
You can put this solution on YOUR website! one number is 16 more than another. If the smaller number is subtracted from two thirds of the larger number, the result is one fourth of the sun of the two numbers. Find the numbers.
Let L = the larger number
Let S = the smaller number
one number, L is 16 more than another, S.
Therefore 
If the smaller number, S, is subtracted from two thirds
of the larger number, that is,   , giving
 , the result is (equals) one fourth
of the sum of the two numbers, that's   .
Therefore,  =.
Simplify by multiplying both sides by the LCD of 
Simplifying further:
Can you solve this system?:
Solution:  , 
Edwin
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