SOLUTION: Nora is twice as old as Raj and half as old as Ethan. In 22 years' time, Ethan will be twice as old as Raj. Find Nora's present age!

Question 1129854: Nora is twice as old as Raj and half as old as Ethan. In 22 years' time, Ethan will be twice as old as Raj. Find Nora's present age!
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!

Nora n
Raj n/2
Ethan 2n
In 22 More Years 2n+22=2(n/2+22)

Nora's age now:

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Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let n = nora's age today, and r = raj's age today and e = ethan's age today.

today, nora is twice as old as raj and half as old as ethan.

you get:

n = 2 * r
n = 1/2 * e

in 22 years, ethan will be twice as old as raj.

you get:

e + 22 = 2 * (r + 22)
simplify to get:
e + 22 = 2 * r + 44

from n = 2 * r, solve for r to get r = 1/2 * n.
from n = 1/2 * e, solve for e to get e = 2 * n.

in e + 22 = 2 * r + 44, replace r with 1/2 * n and replace e with 2 * n to get:

2 * n + 22 = 2 * (1/2 * n) + 44
simplify to get:
2 * n + 22 = n + 44
solve for n to get:
n = 22

your solution looks like it's n = 22.

confirm by finding r and e and then working the problem to see if it's true with those values.

r = 1/2 * n leads to r = 1/2 * 22 = 11
e = 2 * n leads to e = 2 * 22 = 44

currently, ...

n = 22
r = 11
e = 44

in 22 years, ....

n = 44
r = 33
e = 66

in 22 years, e = 2 * r = 2 * 33 = 66, confirming the solution is correct when nora is 22 today.

you basically have equations that need to be solved simultaneously.
i solved using substitution.

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