Question 862659: Together, Grandma and Grandpa are 140 years old. How old is Grandma if Grandpa was twice as old as Grandma was when Grandpa was as old as Grandma is now.
Found 3 solutions by ankor@dixie-net.com, MathTherapy, ikleyn:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Together, Grandma and Grandpa are 140 years old.
How old is Grandma if Grandpa was twice as old as Grandma was when Grandpa was as old as Grandma is now.
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Let m = grandma's age
let p = grandpa's age
:
Let d = the difference in their age d-m
:
"Together, Grandma and Grandpa are 140 years old."
p + m = 140
" How old is Grandma if Grandpa was twice as old as Grandma was when Grandpa was as old as Grandma is now.
Write grandma's age as p-d
p - d = 2(p-d-d)
p - d = 2(p-2d)
p - d = 2p - 4d
4d - d = 2p - p
3d = p
Replace d with (p-m)
3(p-m) = p
3p - 3m = p
3p - p = 3m
3p = 3m
p =  m
p = 1.5m
Replace p with 1.5m in the first equation
1.5m + m = 140
2.5m = 140
m = 140/2.5
m = 56 yrs is Grandma's age
:
:
Check this find Grandpa's age: 1.5(56) = 84 hrs old, 28 yrs apart
"Grandpa was twice as old as Grandma was when Grandpa was as old as Grandma is now."
84 - 28 = 2(56 - 28)
56 = 2(28)
Answer by MathTherapy(10839)  (Show Source):
You can put this solution on YOUR website!
Together, Grandma and Grandpa are 140 years old. How old is Grandma if Grandpa was twice as old as Grandma
was when Grandpa was as old as Grandma is now.
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Let Grandpa's and Grandma's ages, be P, and M, respectively
SInce their ages sum to 140, we get: P + M = 140___M = 140 - P ---- eq (i)
"Grandpa was as old as Grandma is now," clearly signifies that Grandpa is older than Grandma, which means that
the difference in their ages is: P - M
When was Grandpa as old as Grandma is now?
This is the SAME as the difference in their ages, or P - M = P - (140 - P) = P - 140 + P = "2P - 140" years ago
So, when Grandpa was as old as Grandma is now, Grandpa was: M, or "140 - P" years-old
And, when Grandpa was as old as Grandma is now, Grandma was: 140 - P - (2P - 140) = 140 - P - 2P + 140 = - 3P + 280
Finally, since "Grandpa was twice as old as Grandma was when Grandpa was as old as Grandma is now,"
we have: 140 - P = 2(- 3P + 280)
140 - P = - 6p + 560
- P + 6P = 560 - 140
5P = 420
Grandpa's age, or 
Therefore, Grandma is 140 - P = 140 - 84 = 56
Answer by ikleyn(53879)  (Show Source):
You can put this solution on YOUR website! .
Together, Grandma and Grandpa are 140 years old. How old is Grandma if Grandpa was twice as old
as Grandma was when Grandpa was as old as Grandma is now.
~~~~~~~~~~~~~~~~~~~~~~~
Let P be the grandpa age (in years), and
let M be the grandpa age.
First equation is
P + M = 140. (1)
When Grandpa was as old as Grandma ? - It happened (P-M) years ago.
At that time, Grandma was M - (P-M) = 2M - P years old,
while Grandpa was P - (P-M) = M years old.
So, our second equation is
M = 2(2M-P), or M = 4M - 2P, which we transform to 2P = 3M. (2).
So, we transform first equation (1) to
2P + 2M = 280,
and then replace there 2P by 3M, based on (2).
We get then
3M + 2M = 280,
5M = 280,
M = 280/5 = 56.
At this point the solution is complete.
ANSWER. Currently, grandma is 56 years old.
Solved.
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