SOLUTION: Grandpa and his grandson Gary both had their birthday yesterday. Today, grandpa's age in years is an even number and 15 times that of Gary. In 4 years time Grandpa's age in years w

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Question 1206462: Grandpa and his grandson Gary both had their birthday yesterday. Today, grandpa's age in years is an even number and 15 times that of Gary. In 4 years time Grandpa's age in years will be the square of Gary's age in years. How many years older than Gary is grandpa today?
Found 4 solutions by josgarithmetic, mananth, ikleyn, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
system%28v=15j%2Cv%2B4=%28j%2B4%29%5E2%29

15j%2B4=%28j%2B4%29%5E2
15j%2B4=j%5E2%2B8j%2B16
j%5E2-7j%2B12=0
%28j-3%29%28j-4%29=0

j=3------?
------------------------------------------
If j=3, then v=45

j=4------?
If highlight%28j=4%29 then highlight%28v=60%29.
-------------------------------------------

Can those both work?
45+4=(3+4)^2
49=49
cross%28ok%29
-
60+4=(4+4)^2
64=8^2
64=64

Both seem to work.

You can look for the asked-for difference in ages.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Grandpa and his grandson Gary both had their birthday yesterday.
Today, grandpa's age in years is an even number and 15 times that of Gary. In 4 years time Grandpa's age in years will be the square of Gary's age in years. How many years older than Gary is grandpa today?
Let Grandson's age to day be x years
Grandpa's age will be 15x
After 4 years
15x+4 = (x+4)^2
15x +4 = x^2+8x+16
x^2-7x+12=0
x^2-4x-3x+12 =0
x(x-4)-3(x-4)=0
(x-3)(x-4)=0
x = 3 OR 4
Grandson's age is 4
Grandpa's age = 15*4 =60 (Grandpa's age is even)
find the difference


Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.

The notice "Both seem to work." in the post by @josgarithmetic is INCORRECT.

Only the solution "Gary is 4 years old; grandpa is 60 years old" really works,
since the other solution contradicts to the condition
"Today, grandpa's age in years is an even number".

Based on this my correction, you may get the right final answer on your own.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Grandpa's age is an even number that is 15 times his grandson's age. 15 times a whole number being an even number means that whole number is even. So there are only a few reasonable possibilities to check.

grandson 2, grandpa 30: 28 years is too little length for 2 generations; and 30+4=34 is not a perfect square.

grandson 4, grandpa 60: 56 years is a reasonable length for 2 generations; and 60+4 is a perfect square.

grandson 6, grandpa 90: 84 years is PROBABLY too long for 2 generations; and 90+4 is not a perfect square.

So Grandpa is 60 and his grandson is 4; the difference in their ages is 56 years.

ANSWER: 56