Question

Solve this problem in your notebook using all four steps. Harvey is 3 times as old as Jane. The sum of their ages is 48 years. Find the ages of Harvey and Jane. Jane is a0 years old. Harvey is a1 years old.

Answer 1

by saying jane is 1/3 of harvey then J=1/3 H
by removing J and adding the new quantity we git u will got the answer

Answer 2

Jane is 12 years old and Harvey's is 36 years old .

Explanation:

Given :

Jane is
`a_(0)` years old.

Harvey is
`a_(1)` years old.

Harvey is 3 times as old as Jane.

The sum of their ages is 48 years.

To find : The ages of Harvey and Jane.

Solution :

Jane 's age :

`a_(0)`

Harvey 's age:

`a_(1)`

Since we are given that sum of their ages is 48 years

⇒
`a_(1) + a_(0) = 48` ----(A)

We are also given that Harvey is 3 times as old as Jane.

⇒
`a_(1) = 3a_(0)` --- (B)

Solving (A) and (B) using substitution method

Substitute value of
`a_(1)` from (B) in (A) :

⇒
`3a_(0)+ a_(0) = 48`

⇒
`4a_(0) = 48`

⇒
`a_(0) = (48)/(4)`

⇒
`a_(0) = 12`

Thus , Jane 's age is 12 years .

Substitute this value in (B) to find Harvey,s age :

⇒
`a_(1) = 3(12)`

⇒
`a_(1) = 36`

Thus, Harvey,s age is 36 years .

Hence Jane is 12 years old and Harvey's is 36 years old .