SOLUTION: 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

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

RELATED QUESTIONS
Freeda is between 10 and 30 years old. This year her age is a multiple of 7 and next year (answered by Fombitz)

chloe's current age is a multiple of 6. next year, her age will be a multiple of 5. she... (answered by math_tutor2020)

Jane's age is a 2 digit multiple of 4. Next year, her age will be a multiple of 5. How... (answered by Alan3354)

David's age this year is a multiple of 5. Next year David's age will be a multiple of 7.... (answered by stanbon)

Susie's age this year is a multiple of 5. Next year, her age is a multiple of 7. What is... (answered by ikleyn,MathTherapy)

alice is between 20 and 40 years old. last year, her age was a multiple of 4. this year, (answered by srinivas.g)

your fathers age this year is a multiple of 5. Next year his age will be a multiple of 6. (answered by Alan3354,ikleyn)

My age this year is a multiple of 8.Next year it will be a multiple of 7.How old am... (answered by Edwin McCravy,KMST)

mother's age this year is multiple of 5. last year her age was a multiple of 3. she is... (answered by josgarithmetic)