how old are they?

Question

gradma and gradpa together are 140 years old. how old is each of them if grandpa is twice much old as gradma was when he was as old as she is now.
we had to solve this at school when we were13 years old!!!!!!!!!!
simply mad! can you solve it?

Answer 1

Let grandma's age be m and grandpa's p.
How many years ago was it when grandpa was as old as
she is now. Well is p-m of course. And she was m-(p-m)
then. So he's
p=2(m-(p-m))
p=2(2m-p)
p=4m-2p and since m=140-p
p=4(140-p)-2p=560-6p
7p=560
p=80, so m=60 based on 80+60=140
Checking: when he was 60, she was 40, as which ,
80 is twice as much.

Answer 2

If at this point the male and female both are aged 140, we need to calculate at what point the GP was twice the age of the GM and then add that age to the total of the GP at that point and the GM at that point then add the two together and this should be 140
We can calculate that the age when the GP was 2xGM age was 1/5 of the total at this point
THEREFORE
140 ÷ 5 = 28
so 28 years ago or 140 - (28 x 2) the sum age would be 84
If we now divide 84 by 3 we reach the conclusion that they were 56 & 28 at that point so we now add 28 to both ages and thus we get 84 & 56 which total 140 thus proving our theory
Another way to reach this conclusion is to consider the following

140 ÷ 3 leaves a fraction
140 ÷ 4 = 35 but 35 years ago the two Mature people would be 70 years younger in total thus 70 yaers between them and yet they are sharing 3 total ages together thus this does not work as it leaves a fraction.
Then we use 140 ÷ 5 which in turn gives us 28 which if we double and take from 140 leaves us with a number divisible by 3 and this once again proves our hypothesis to be correct

Answer 3

Let grandma's age then be x and now be x+a.

So grandpa's age then is x+a and now be x+2a.

(x+a)+(x+2a) = 140
2x = x+a

So 2x = x+a => 2x-x = a => x = a

Hence, (x+x)+(x+2x) = 140 => 5x = 140 => x = 28.

So grandma is x+a = x+x = 28 + 28 = 56
and grandpa is x+2a = x+2x = 3x = 3(28) = 84

Answer 4

Well I got, grandpa 84 and grandma 56
I am doing a degree in computer science which includes alot of advanced maths, so if I got this wrong, and you got it at 13, well done!!!!!!

Answer 5

I make it 47 and 94 too. Both answers have been rounded up to the nearest whole numbers.

Answer 6

here it goes:
male = m, female = f

m+f=140

(m-x) = f (x years ago male was as female is NOW)
(m-x) = 2 * (f-x) (he was then 2 times older)
-----------------------------------
m-x = 2 * [ (m - x) - x]
therefore ... m - x = 2m - 4x
m = 3x
f = m - x = 2x

therefore ... m + f = 3x + 2x = 5x
5x = 140 -> x = 28

so, grandpa was as old as grandma 28 years ago.

so, m - 28 = f
-> m + (m-28) = 140 ---> 2m = 168 -> m = 84 -> f=56

28 years ago, he was 56 and she was 28

good for him

Answer 7

I could have answered it at 13 too but now I'm old and have drunk a lot of wine my brain cells have all gone. My cat's 11 though!!!

Answer 8

Grandma is 47years old(i rounded to the nearest whole number) and grandpa is 94 years old(also round up)....

Grandpa is a PIMP

Answer 9

if he is now twice her age then and was then her age now, then he's 80 and she's 60.
a+b=140
a-c=b -> a=b+c
a=2(b-c)
b+c=2b-2c
b=3c
a=b+c=4c
140=7c
c=20 b=60 a=80

Answer 10

well!
70 and 70