Question 1060534
Let {{{ a }}} = the larger number 
Let {{{ b }}} = the smaller number
--------------------------------
(1) {{{ a = 5b }}}
(2) {{{ 1/a + 1/b = 6/35 }}}
---------------------------
Substitute (1) into (2)
(2) {{{ 1/(5b) + 1/b = 6/35 }}}
Multiply both sides by {{{ 5b }}}
(2) {{{ 1 + 5 = 30b/35 }}}
(2) {{{ 6*35 = 30b }}}
(2) {{{ 30b = 210 }}}
(2) {{{ b = 7 }}}
and
(1) {{{ a = 5b }}}
(1) {{{ a = 5*7 }}}
(1) {{{ a = 35 }}}
--------------------
The 1st number is 35
The 2nd number is 7
---------------------
check:
(2) {{{ 1/a + 1/b = 6/35 }}}
(2) {{{ 1/35 + 1/7 = 6/35 }}}
(2) {{{ 1/35 + 5/35 = 6/35 }}}
(2) {{{ 6/35 = 6/35 }}}
OK