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):
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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