Question 952520: 20 years ago Grandma was twice as old as Mum. Today, Grandma is twice the age Mum was when I was born. How old am I?
Found 2 solutions by ankor@dixie-net.com, MathTherapy:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! let g = Grandma's age
let m = Mom's age
let y = your age
:
Write an equation for each statement
:
20 years ago Grandma was twice as old as Mum.
g - 20 = 2(m-20)
g - 20 = 2m - 40
g = 2m - 40 + 20
g = 2m - 20
:
Today, Grandma is twice the age Mum was when I was born.
g = 2(m-y)
g = 2m - 2y
:
g = g
2m - 20 = 2m - 2y
Subtract 2m from both sides
-20 = -2y
y = -20/-2
y = 10 yrs old is your age
Answer by MathTherapy(10839)  (Show Source):
You can put this solution on YOUR website!
20 years ago Grandma was twice as old as Mum. Today, Grandma is twice the age Mum was when I was born. How old am I?
**************************************
Let Grandma's current age, be G, and Mum's, M
Then 20 years ago Grandma was G - 20, and Mum was M - 20
Given that, "20 years ago Grandma was twice as old as Mum," gives us:
G - 20 = 2(M - 20) ===> G - 20 = 2M - 40 ===> G = 2M - 40 + 20 ===> G = 2M - 20 ---- eq (i)
G - 20 = 2(M - 20) ===> G - 20 = 2M - 40____G - 20 + 40 = 2M ===> G + 20 = 2M ====>  ----- eq (ii)
Let the number of years since my birth, be y
Mum's age, when I ws born: M - y, or 
"Today, Grandma is twice the age Mum was when I was born," gives us: G = 2(M - y)
 ----- Substituting  for M
G = G + 20 - 2y
G - G - 20 = - 2y ---- Subtracting 20 from each side
- 20 = - 2y
Years since I was born/my age, or 
|
|
|
