Question 1070012
ONE WAY:
The multiples of 7 between 20 and 70 are
21, 28, 35, 42, 49, 56, 63,
(and if it was between 20 and 70 inclusive,
also 70.
35 and 7p are multiples of 5,
and would not be if wee add 3.
The other numbers, with 3 added are
24, 31, 45, 52, 59, and 66.
The only one of those that is s multiple of 5
is {{{42}}} , and in {{{6}}} years
he will be {{{42=6+highlight(48)}}} ,
so John is 42.
 
A FANCY WAY:
{{{7n}}}= John's age now,
with {{{n}}} being a whole number.
We are told that {{{20<=7n<=70}}} ,
so {{{20/7<=n<=70/7}}}-->{{{3<=n<=10}}} .
{{{7n+3}}}= John's age in {{{3}} years.
{{{7n+3=5n+2n+3=5n+2(n-1)+2+3=5n+5+2(n-1)}}}
The only way that sum can be a multiple of {{{5}}}
is of {{{2(n-1)}}} , and therefore {{{n-1}}}
are multiples off {{{5}}} ,
and with {{{3<=n<=10}}}<-->{{{2<=n-1<=9}}} ,
the only choice is {{{n-1=5}}} .
So, {{{n=5+1=6}}} and {{{7n=7*6=42}}} .
In 6 years time, John will be
{{{42+6=highlight(48)}}} .