Question 700954
Let the numbers = {{{ x }}} and {{{ y }}}
given:
(1) {{{ x + y = 55 }}}
Assume that {{{ y }}} is the larger number
(2) {{{ y/x = 2 + 7/x }}}
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Multiply both sides of (2) by {{{ x }}}
(2) {{{ y = 2x + 7 }}}
(2) {{{ -2x + y = 7 }}}
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Subtract (2) from (1)
(1) {{{ x + y = 55 }}}
(2) {{{ 2x - y = -7 }}}
{{{ 3x = 48 }}}
{{{ x = 16 }}}
and, since
(2) {{{ y = 2x + 7 }}}
(2) {{{ y = 2*16 + 7 }}}
(2) {{{ y = 39 }}}
The numbers are 16 and 39
check:
(2) {{{ y/x = 2 + 7/x }}}
(2) {{{ 39/16 = 2 + 7/16 }}}
(2) {{{ 39 = 2*16 + 7 }}}
(2) {{{ 39 = 32 + 7 }}}
(2) {{{ 39 = 39 }}}
OK