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.
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Let L = the larger number
Let S = the smaller number

one number, L is 16 more than another, S. 

Therefore {{{L = S + 16}}}

If the smaller number, S, is subtracted from two thirds
of the larger number, that is, {{{2/3}}}{{{L}}}, giving 
{{{2/3}}}{{{(L-S)}}}, the result is (equals) one fourth
of the sum of the two numbers, that's {{{1/4}}}{{{(L+S)}}}. 

Therefore, {{{2/3}}}{{{L-S}}}={{{1/4}}}{{{(L+S)}}}. 

Simplify by multiplying both sides by the LCD of {{{12}}}

{{{(12)(2/3)L-(12)S=(12)(1/4)(L+S)}}}

Simplifying further:

{{{8L-12S=3(L+S)}}}
{{{8L-12S=3L+3S}}}
{{{5L=15S}}}
{{{L=3S}}}

Can you solve this system?:

{{{system(L = S + 16,L=3S)}}}

Solution: {{{L=24}}}, {{{S=6}}}

Edwin</pre>