SOLUTION: 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 differe

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(52793) (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?
~~~~~~~~~~~~~~~

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.

-------------

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.

RELATED QUESTIONS
Lisa’s age is twice her sisters age. The difference between their ages is eight. How... (answered by mananth,math_helper)
Tim and Tala are brother and sister. Their ages total 36. The difference between twice... (answered by ikleyn,josgarithmetic,greenestamps)
a mother’s age is 13 years older than twice her daughters age. if the difference of... (answered by josgarithmetic)
Kim is half her father's age. The difference in their ages is 25 years. How old is... (answered by josgarithmetic)
[ A boy observed that twice his age is 5 more years than his older sister's. His sister... (answered by TimothyLamb)
If Maria age is 8 which is a quarter of her sister's age.what is their age in... (answered by math_tutor2020,josgarithmetic)
Noelle is 5 years younger than her sister Aya. The difference of the square of Aya’s... (answered by josgarithmetic)
If 3 times Jane�s age, in years, is equal to 8 times Beth�s age, in years, and the... (answered by jojo14344)
The ratio of johm�s ages to his sons age is 8:3 . if the sum of their ages is 55 years ,... (answered by ankor@dixie-net.com)