Question

Alisha is 9 years younger than Joanne. In 5 years’ time Joanne will be twice as old as Alisha. How old will Alisha be after 15 years?

Answer 1

Answer:

Alisha will be 19 years old.

Step-by-step explanation:

Given :

Alisha is = 9 years younger than Joanne

After 5 years = Joanne will be twice the age of Alisha

To find :

Alisha's age after 15 years

Solution :

Let the present ages be -

• Joanne as x
• Alisha as (x - 9)

Ages after 5 years -

• Joanne = (x + 5)
• Alisha = (9 - x) + 5

$\rule{300}{1.5}$

According to the question, Joanne will be twice the age of Alisha after 5 years,

$\sf{\longrightarrow} \: x + 5 = 2(x - 9) + 5 \\ \\ \sf{\longrightarrow} \: x + 5 = 2x - 18 + 10 \\ \\ \sf{\longrightarrow} \: x + 5 = 2x - 8 \\ \\\sf{\longrightarrow} \: x - 2x = - 8 - 5 \\ \\ \sf{\longrightarrow} \: x = 13$

Joanne's present age = 13 years

$\rule{300}{1.5}$

★ Alisha's present age -

$\sf{\longrightarrow} \: 13 - 9 \\ \\ \sf{\longrightarrow} \: 4$

Alisha is presently 4 years old.

$\rule{300}{1.5}$

★ Alisha's age after 15 years -

$\sf{\longrightarrow} \: 4 + 15 \\ \\ \sf{\longrightarrow} \: 19$

Alisha's age after 15 years is 19 years.

$\therefore$ Alisha will be 19 years old.

Answer 2

Answer:

$\large{\underline{\boxed{\mathfrak\blue{Age \: of \: Alisha \: after \: 15 \: years = 19 \: years}}}}$

Given:-

• Age of Alisha = Joanne's present age - 9

• In 5 years, Joanne's age = 2 × Alisha's age

To find:-

• Age of Alisha after 5 years = ?

Let present ages of Alisha and Joanne be a & b years respectively.

A/Q,

$\: \: \: \: \: \: \dashrightarrow\sf a = b - 9 \\\\ \: \: \: \: \: \: \dashrightarrow\sf a - b = - 9 \: \: \: \: \: \:-(eq.1)$

Secondly,

$\: \: \: \: \: \:\dashrightarrow\sf b + 5 = 2(a + 5) \\\\ \: \: \: \: \: \:\dashrightarrow\sf b + 5 = 2a + 10 \\\\ \: \: \: \: \: \:\dashrightarrow\sf 2a - b = 5 - 10 \\\\ \: \: \: \: \: \: \dashrightarrow\sf 2a - b = - 5 \: \: \: \: \: \: -(eq.2)$

Substracting (eq.2) from (eq.1) :-

$\: \: \: \: \: \: \dashrightarrow\sf a - b - 2a + b = - 9 + 5$

$\: \: \: \: \: \: \dashrightarrow\sf - a = - 4$

$\: \: \: \: \: \:\dashrightarrow\large{\underline{\boxed{\sf\blue{ a = 4 }}}}$

$\therefore{\underline{\text{Present \: age \: of \: Alisha = 4 \: years }}}$

• Putting value of a in (eq.1) :-

$\: \: \: \: \: \: \dashrightarrow\sf 4 = b - 9 \\\\ \: \: \: \: \: \: \dashrightarrow\sf b - 9 - 4 = 0 \\\\ \: \: \: \: \: \: \dashrightarrow\sf b - 13 = 0 \\\\ \: \: \: \: \: \: \dashrightarrow\large{\underline{\boxed{\sf\green{b = 13 \: years }}}}$

$\therefore{\underline{\text{Present \: age \: of \: Joanne = 13 \: years }}}$

Now,age of Alisha after 15 years,

$\: \: \: \: \dashrightarrow\sf Age \: of \: Alisha = (4 + 15) \: years \\\\ \: \: \: \: \dashrightarrow\large{\underline{\boxed{\sf\purple{Age \: of \: Alisha = 19 \: years }}}}$

$\therefore\: \: {\boxed{\text{Age \: of \: Alisha \: after \: 15 \: years = 19 \: years }}}$