Question 972804
The present ages of a husband and wife are in the ratio of seven to six,
 and five years ago the ratio was six to five.
 Find their ages now.
:
let x = the multiplier
then
7x = husband's age now
6x = wife's age now
:
" five years ago the ratio was six to five.
{{{((7x-5))/((6x-5))}}} = {{{6/5}}}
cross multiply
6(6x-5) = 5(7x-5)
36x - 30 = 35x - 25
36s - 35x = -25 + 30
x = 5 is the multiplier
therefore
5(7) = 35 is husband's age
and
5(6) = 30 is wife's age
:
:
See if that checks out in the statement
"five years ago the ratio was six to five.
{{{((35-5))/((30-5))}}} = 
{{{30/25}}} = {{{6/5}}}