Question 9536: Ann's age this year is a multiple of 7. Next year her age will be a multiple of 4. Her age is between 10 and 60. Hoe old is Ann Answer by mathmaven53(29) (Show Source):
You can put this solution on YOUR website! Let A be her age this year then A = 7k for some positive integer k
A+1 is her age next year and A+1 = 4l for some positive integer l
1 = A+1 -A
= 4l - 7k
We have to solve 4l - 7k = 1 in positive integers
We write equivalently 4l -8k + k = 1
4l - 8k = 1 -k
Let 1-k = 4r for some integer r
Then k = 1 -4r
Substitute for k and solve for l in 4l - 7k = 1
We get l = 2-7r
A = 7k
= 7 -28r
10 < A < 60
By substituting for A and solving for r we get
-53/28 < r < -3/28
The only integer that satisfies this is r=-1
Then A = 7-28r
= 35
Ann is 35 this year which is a multiple of 7
next year she is 36 which is a multiple of 4
and 35 is between 10 and 60
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