SOLUTION: One number is 16 more than the other. If the smaller number is subtracted from two thirds of the larger, the result is one fourth of the sum of the two numbers. Find the numbers.

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: One number is 16 more than the other. If the smaller number is subtracted from two thirds of the larger, the result is one fourth of the sum of the two numbers. Find the numbers.      Log On


   

Question 175389: One number is 16 more than the other. If the smaller number is subtracted from two thirds of the larger, the result is one fourth of the sum of the two numbers. Find the numbers.
Found 2 solutions by josmiceli, adrian13r:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the larger number a
Call the smaller number b
Given:
(1) a+=+b+%2B+16
(2) %282%2F3%29%2Aa+-+b+=+%281%2F4%29%28a+%2B+b%29
multiply both sides by 12
8a+-+12b+=+3a+%2B+3b
5a+=+15b
a+=+3b
Substitute this value for a in (1)
3b+=+b+%2B+16
2b+=+16
b+=+8
and
a+=+3b
a+=+24
Yhe numbers are 24 and 8
check:
(2) %282%2F3%29%2Aa+-+b+=+%281%2F4%29%28a+%2B+b%29
%282%2F3%29%2A24+-+8+=+%281%2F4%29%2824+%2B+8%29
16+-+8+=+%281%2F4%29%2A32
8+=+8
OK

Answer by adrian13r(5) About Me  (Show Source):
You can put this solution on YOUR website!
This is actually very simple. In "reading between the lines" you must realize that the bigger number is going to be a factor of 3. In doing a little math, you arrive to an answer of the smaller number being 8 and the bigger number being 24.