Question 108129: I am trying to help my daughter but we cannot set up this problem can you please help us thank you.
For six consecutive years a man's age was a multiple of his granddaugters age. How old was each during the sixth year?
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! Let's call the Grandfather's age, X, and the Grandaughter's age Y.
The first year X=mY where m is an integer (1,2,3,4,..)
and for the next 5 years,
X+1=n(Y+1)
X+2=o(Y+2)
X+3=p(Y+3)
X+4=q(Y+4)
X+5=r(Y+5)
where n,o,p,q,and r are also integers.
Using this method you have 6 equations, but you have 8 unknowns, so it doesn't help.
Another method is to look at the list of prime numbers, that is numbers that are divisible only by themselves and 1.
You need to find 6 consecutive non-prime or composite numbers.
The list of primes under 100 is
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
The first time you have six consecutive divisible numbers starts at 90.
90=3x3x10
91=7x13
92=2x2x23
93=3x31
94=2x47
95=5x19
96=2x2x24
The issue is that 93,94,95 have only prime factors and the factors are not consecutive, so they can't be the daughter's age.
The next 6 consecutive composite numbers start at 114 to 126.
The same issue exists as before
115,118,119,122,123,124 have large prime factors in them and cannot be the daughter's age.
I don't believe there's a solution to this problem, as stated.
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