Question

2. Jane is now four times as old as Rita.

In 6 years, Jane will be only twice as
old as Rita at that time. Find their
present ages.

Answer 1

Let's start by using algebra to solve the problem.

Let's assume that Rita's age is x.

According to the problem, Jane is four times as old as Rita, so her age is 4x.

In 6 years, Jane will be twice as old as Rita at that time. This means that:

4x + 6 = 2(x + 6)

Simplifying this equation:

4x + 6 = 2x + 12

2x = 6

x = 3

This means that Rita is currently 3 years old.

To find Jane's age, we can use the equation we derived earlier:

Jane's age = 4x = 4(3) = 12

Therefore, Jane is currently 12 years old and Rita is currently 3 years old.

Answer 2

Rita's age = 3 years

Jane's age = 12 years

Explanation:

Framing algebraic equations and solving:

Let the age of Rita = x years

Age of Jane = 4 times of Rita's age

= 4*x

= 4x

After 6 years,

Jane's age = 4x + 6

Rita's age = x + 6

Jane's age = twice of Rita's age

4x + 6 = 2* (x + 6)

4x + 6 = 2x + 12 {Distributive property}

Subtract 6 from both sides,

4x = 2x + 12 - 6

4x = 2x + 6

Subtract '2x' from both sides,

4x - 2x = 6

2x = 6

Divide both sides by 2,

x = 6 ÷ 2

x = 3

Rita's age = 3 years

Jane's age = 4 * 3

= 12 years