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

Eureka's Age:
Renton's Age:

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.

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

To solve this problem, let's assign variables to represent the ages of Eureka and Renton. Let's say Eureka's age is represented by the variable "E," and Renton's age is represented by the variable "R."

From the information given, we can deduce two equations:

1) Eureka is 16 years younger than Renton:
E = R - 16

2) In 3 years, Renton will be twice as old as Eureka:
R + 3 = 2(E + 3)

Now, we have a system of two equations:

Equation 1: E = R - 16
Equation 2: R + 3 = 2(E + 3)

We can solve this system of equations to determine the ages of Eureka and Renton.

First, let's substitute Equation 1 into Equation 2:

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

Simplifying this equation:

R + 3 = 2(R - 13)
R + 3 = 2R - 26

Bringing all terms to one side of the equation:

2R - R = 3 + 26

R = 29

Now, substituting this value back into Equation 1 to find Eureka's age:

E = R - 16
E = 29 - 16
E = 13

Therefore, Eureka is currently 13 years old and Renton is currently 29 years old.