Question 168241
Call the larger number {{{a}}}
Call the smaller number {{{b}}}
Given:
(1) {{{a = b + 7}}}
(2) {{{3a = 4b + 5}}}
Substitute {{{a}}} in (1) for {{{a}}} in (2)
(2) {{{3*(b + 7) = 4b + 5}}}
{{{3b + 21 = 4b + 5}}}
Subtract {{{3b}}} from both sides
Subtract {{{5}}} from both sides
{{{b = 16}}}
and, since
(1) {{{a = b + 7}}}
{{{a = 16 + 7}}}
{{{a = 23}}}
The larger number is 23 and the smaller number is 16
check:
(1) {{{a = b + 7}}}
{{{23 = 16 + 7}}}
{{{23 = 23}}}
(2) {{{3a = 4b + 5}}}
{{{3*23 = 4*16 + 5}}}
{{{69 = 64 + 5}}}
{{{69 = 69}}}
OK