Question

Three years ago Tom was twice as old as Jean. And in two years the sum of their ages will be 28 years. Find their present ages.

Answer 1

Answer:

Jean is 9 years old and Tom is 15 years old.

Step-by-step explanation:

let t = Tom's present age

let j = Jean's age

Three years ago, Tom was twice as old as Jean,

t-3 = 2(j-3)

t - 3 = 2j - 6

t = 2j - 6 + 3

t = 2j - 3

In two years the sum of their ages will be 28 years.

(t+2) + (j+2) = 28

t + j + 4 = 28

t + j = 28 - 4

t + j = 24

For their present ages, replace t with (2j-3) from the 1st statement

2j - 3 + j = 24

2j + j = 24 + 3

3j = 27

j = 27/3

j = 9 yrs is Jean's age

Find Tom's age

t = 2(9) - 3

t = 15 yrs is Tom's age

Answer 2

An equation is formed of two equal expressions. The age of Tom is 15 years and the age of Jean is 9 years.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the present age of Tom and Jean be represented by x and y, respectively. Therefore, the given statement three years ago Tom was twice as old as Jean in the form of an equation can be written as,

(x-3) = 2(y-3)

Solving the equation for x,

x - 3 = 2y - 6

x = 2y - 3

Also, it is given that in two years the sum of their ages will be 28 years.

(x+2) + (y+2) = 28

(2y - 3 + 2) + (y + 2) = 28

2y -3 + 2 + y + 2 = 28

3y + 1 = 28

3y = 27

y = 9

Substitute the value of y in the equation of x formed above,

x = 2y - 3

x = 2(9) - 3

x = 15

Hence, the age of Tom is 15 years and the age of Jean is 9 years.

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