SOLUTION: the sum of my parents' ages is 70. Twenty years ago, my father was 4 years older than my mother. how old are they now

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Question 1062268: the sum of my parents' ages is 70. Twenty years ago, my father was 4 years older than my mother. how old are they now
Found 2 solutions by Cromlix, MathTherapy:
Answer by Cromlix(4381)   (Show Source): You can put this solution on YOUR website!
Hi there,
the sum of my parents' ages is 70
Father = x
Mother = y
x + y = 70........Eq(1)
x = 70 - y........Eq(1)
Twenty years ago, my father was 4 years
older than my mother.
x - 20 = 4 + (y - 20)........Eq(2)
Replace x in Eq(2) with 70 - y
(70 - y) - 20 = 4 + (y - 20)......Eq(2)
70 - y - 20 = 4 + y - 20
Collect like terms
- y - y = 4 - 20 + 20 - 70
-2y = -66
Multiply both sides by -1
2y = 66
y = 33
Substitute y = 33 into Eq(1)
x + y = 70.........(1)
x + 33 = 70
x = 70 - 33
x = 37
Mother is 33 years old
Father is 37 years old.
Hope this helps :-)
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

the sum of my parents' ages is 70. Twenty years ago, my father was 4 years older than my mother. how old are they now
Let father's age be F

Then mother's age = 70 - F

Father was 4 years older than mother, 20, 10, 5, 2, 15 years ago. The point is, while alive, the father will always be 4 years older than the mother. 

Hence, we get mother's age as: F - 4

We then have: 70 - F = F - 4

- F - F = - 4 - 70

- 2F = - 74

F, or father's age is: 

Mother's is: 70 - 37, or 37 - 4 =  

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