Terry is 24 years old. She was twice as old as Ellen was when she was as old as Ellen is now? How old is Ellen?

Answer 1

This seems difficult at first, but we need to find a system of equations that we can solve for the unknowns. What we don't know is Ellen's age now and the difference in the girls' ages.

Let x= Ellen's present age

y= difference in their ages

We know that Terry is 24, so that means that Ellen's age, x, plus the difference in their ages, y, must equal 24:

Eq. I: x+y=24

We also know that when Terry was Ellen's age now, 24-y, she was twice Ellen's age then, 2(x-y):

Eq. II: 24-y=2x-2y

2y-y=2x-24

y=2x-24

Substituting the value for y from Eq. II into Eq. I we can solve for x:

x+y=24 Eq. I

x+(2x-24)=24 substitute value for y from Eq. II

3x=24+24

3x=48

x=16

Therefore, Ellen's present age is 16.

Answer 2

We have to first differentiate between the present and the past ages in this problem.

Let's say the past ages are the ages now minus y years that have passed:

Ellen's age now = x

Ellen's age in the past = x - y

Terry's age in the past = 24 - y

The problem tells us that:

(1) Terry's age in the past is equal to Ellen's age now: 24 - y = x

(2) Terry's age in the past is 2 times Ellen's age in the past: 24 - y = 2(x - y)

Rearrange (1):

y = 24 - x

Substitute the above into (2):

24 - (24 - x) = 2[x - (24 - x)]

Simplify:

x = 2(2x - 24)

x = 4x - 48

48 = 3x

x = 16

So, Ellen is currently 16 years old.