Eureka is 16 years younger than Renton. In 3 years Renton will be twice as old as Eureka. How old are they now?

Question

Eureka's Age:
Renton's Age:

Answer 1

E = Eureka's Age

R = Renton's Age

E = R - 16

In 3 years Renton will be R + 3

Eureca will be E + 3

In 3 years Renton will be twice as old as Eureka.

This mean :

R + 3 = 2 ( E + 3 )

R + 3 = 2 ( R - 16 + 3 )

R + 3 = 2 ( R - 13 )

R + 3 = 2 R - 26 Add 26 to both sies

R + 3 + 26 = 2 R - 26 + 26

R + 29 = 2 R Subtract R to both sides

R + 29 - R = 2 R - R

29 = R

R = 29

E = R - 16

E = 29 - 16

E = 13

Eureka's Age = 13

Renton's Age = 29

Proof :

In 3 years Renton will be 32

Eureca will be 16

32 / 16 = 2

Renton will be twice as old as Eureka.

Answer 2

Let y be Eureka's age in years.
Let x be Renton's age in years.

So:
y = x-16
2(y+3) = x+3

Rearrange to express x as a function of y.
x = y + 16
x = 2y + 3

Eliminating x by equating:
y + 16 = 2y +3
=> y = 13

Substituting back to obtain x.
x = 13 + 16
=> x = 29