Question

I am three times as old as you were when I was as old as you are. The sum of my age and your age is fifty. what is my age? *

Answer 1

Answer:

am three times as old as you were when I was as old as you are now.

When you got to be my age together our ages will be 84.

How old are we now?

:

Let x = my present age

Let y = your present age

then

(x-y) the difference in the ages

:

"I am three times as old as you were when I was as old as you are now."

x = 3[y - (x - y)]

x = 3(y - x + y)

x = 3(2y - x)

x = 6y - 3x

x + 3x = 6y

4x = 6y

:

" When you got to be my age together our ages will be 84."

x + x +(x-y) = 84

3x - y = 84

-y = -3x + 84

y = (3x - 84)

:

Substitute (3x-84) for y in the equation: 4x = 6y

4x = 6(3x-84)

4x = 18x - 504

504 = 18x - 4x

504 = 14x

x = 504%2F14

x = 36 is my age

then

4(36) = 6y

144 = 6y

y = 144%2F6

y = 24

:

Check solution

36 - 24 = 12 is the age difference

:

"I am three times as old as you were when I was as old as you are now."

36 = 3(24 - 12)

36 = 3(12)

:

"When you got to be my age together our ages will be 84.

36 + (36 + 12) = 84

:

I am 36 and you are 24