SOLUTION: Alvin is 5/6 of Chris's age. In 10 years time, their total age will be 42. What is the ratio of alvin to chris's age 11 years from now?

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Question 1120649: Alvin is 5/6 of Chris's age. In 10 years time, their total age will be 42. What is the ratio of alvin to chris's age 11 years from now?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
a, Alvin
c, Chris
system%28a=%285%2F6%29c%2C%28a%2B10%29%2B%28c%2B10%29=42%29
-
system%286a=5c%2Ca%2Bc=42-20%29

system%28a%2Bc=22%2C6a=5c%29

6a=5%2822-a%29

6a=110-5a
11a=110


system%28NOW%2Ca=10%2Cc=12%29

Eleven years from now, ratio of their ages:
%2810%2B11%29%2F%2812%2B11%29, Alvin to Chris

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


If an algebraic solution is required, then you need to go with something like the other tutor showed.

But if you can get the answer any way you want, and as quickly as possible, then a purely algebraic solution is way too much work.

Use some logical reasoning and a bit of mental arithmetic.

(1) If their total age 10 years from now will be 42, then their total age now is 22.
(2) If their total age now is 22 and the ratio of Alvin's age to Chris's age is 5:6, a very little mental arithmetic tells us that now Alvin is 10 and Chris is 12.
(3) So 11 years from now their ages will be 21 and 23; the ratio of their ages will be 21:23.