Question 1190940: Linda's age is twice her sister's age. Difference between their ages is a perfect square number. If the difference in their age is between 5 years and 40 years, what is the difference between the highest and the lowest possible values of Linda's age?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Edit: I changed the 40 to 36. I'm not sure why my brain went for that error initially.
Difference between their ages is a perfect square number.
The difference in their age is between 5 years and 40 years.
Those two facts allow us to say that their age gap is one of the following numbers: 9, 16, 25, 36
Simply list the perfect squares between 5 and 40.
Later on, we'll only focus on the smallest and largest age gap.
x = sister's present day age
2x = Linda's present day age
If Linda is 9 years older, then
(linda's age) - (sister's age) = 9
2x - x = 9
x = 9
Telling us that the sister is 9 years old and Linda is 2*x = 2*9 = 18 years old.
Or if Linda is 36 years older, then you should find that x = 36 through similar steps. That would make Linda to be 2x = 2*36 = 72 years old.
Linda's lowest age = 18
Linda's highest age = 80
Difference = 72 - 18 = 54
Answer: 54
Answer by ikleyn(52878)  (Show Source):
You can put this solution on YOUR website! .
Linda's age is twice her sister's age.
Difference between their ages is a perfect square number.
If the difference in their age is between 5 years and 40 years,
what is the difference between the highest and the lowest possible values of Linda's age?
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Let x be the sister's age.
Then the Linda's age is 2x, according to the problem.
The difference of their ages 2x-x = x is the perfect square number between 5 and 40.
So, x is one of the numbers 9, 16, 25, 36.
Thus the minimum Landa's age is 2*9 = 18 years, and the maximum Linda's age is 2*36 = 72 years.
The difference between the highest and the lowest possible values of Linda's age is 72 - 18 = 54 years.
Solved.
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This problem is presented as a Math problem, so, my major concern is to make it logically consistent.
I do not go in discussing whether it is realistic to have a difference of ages of 36 years between the sisters.
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