SOLUTION: john age is a multiple of 7 this year. in 3 years time, his age will be a muiltiple of 5. his age is between 20 and 70, how old will john be in 6 years time?

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Question 1070012: john age is a multiple of 7 this year. in 3 years time, his age will be a muiltiple of 5. his age is between 20 and 70, how old will john be in 6 years time?
Answer by KMST(5328) About Me  (Show Source):
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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%2Bhighlight%2848%29 ,
so John is 42.

A FANCY WAY:
7n= John's age now,
with n being a whole number.
We are told that 20%3C=7n%3C=70 ,
so 20%2F7%3C=n%3C=70%2F7-->3%3C=n%3C=10 .
7n%2B3= John's age in 3%7D%7D+years.%0D%0A%7B%7B%7B7n%2B3=5n%2B2n%2B3=5n%2B2%28n-1%29%2B2%2B3=5n%2B5%2B2%28n-1%29
The only way that sum can be a multiple of 5
is of 2%28n-1%29 , and therefore n-1
are multiples off 5 ,
and with 3%3C=n%3C=10<-->2%3C=n-1%3C=9 ,
the only choice is n-1=5 .
So, n=5%2B1=6 and 7n=7%2A6=42 .
In 6 years time, John will be
42%2B6=highlight%2848%29 .