SOLUTION: Kei is twice as old as Mira. In three years, the sum of their ages will be four times as much as Kei’s age 6 years ago. How old is Mira?

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Question 949416: Kei is twice as old as Mira. In three years, the sum of their ages will be four times as much as Kei’s age 6 years ago. How old is Mira?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
let's say Kei is x years old and Mira is y years old
if Kei is twice as old as Mira, then we have:
x=2y......eq.1
In three years, they will be x%2B3 and y%2B3 years old
the sum of their ages will be
%28x%2B3%29%2B%28y%2B3%29

four times as much as Kei’s age 6 years ago, 4%28x-6%29
so, the sum is:
%28x%2B3%29%2B%28y%2B3%29=4%28x-6%29 ......eq.2
substitute x from eq.1
%282y%2B3%29%2B%28y%2B3%29=4%282y-6%29 ......eq.2....solve for y
2y%2B3%2By%2B3=8y-24
3y%2B6=8y-24
24%2B6=8y-3y
30=5y
30%2F5=y
highlight%28y=6%29
Mira is highlight%286%29 years old.
and Kei is highlight%2812%29 years old