Question 175389
Call the larger number {{{a}}}
Call the smaller number {{{b}}}
Given:
(1) {{{a = b + 16}}}
(2) {{{(2/3)*a - b = (1/4)(a + b)}}}
multiply both sides by {{{12}}}
{{{8a - 12b = 3a + 3b}}}
{{{5a = 15b}}}
{{{a = 3b}}}
Substitute this value for {{{a}}} in (1)
{{{3b = b + 16}}}
{{{2b = 16}}}
{{{b = 8}}}
and
{{{a = 3b}}}
{{{a = 24}}}
Yhe numbers are 24 and 8
check:
(2) {{{(2/3)*a - b = (1/4)(a + b)}}}
{{{(2/3)*24 - 8 = (1/4)(24 + 8)}}}
{{{16 - 8 = (1/4)*32}}}
{{{8 = 8}}}
OK