Question

Ava has $110 in her piggy bank and spends $5 a week. Liam has $20 in his piggy bank and does chores to earn an extra $4 a week. When will Ava and Liam have the same amount of money ?

Answer 1

Ava and Liam have the same amount of money at 10th week.

Explanation:

Given:

Amount Ava has in her piggy bank = $110

Amount spends per week = $5

Let the number of weeks be 'w'.

So we can say that.

Total amount Ava had after 'w' weeks =
`110-5w`

Also Given:

Amount Liam has in her piggy bank = $20

Amount earns per week = $4

Let the number of weeks be 'w'.

So we can say that.

Total amount Liam had after 'w' weeks =
`20+4w`

Now we need to find the number of weeks when both will have same amount.

So we can say that;

Total amount Ava had after 'w' weeks =Total amount Liam had after 'w' weeks

`110-5w=20+4w`

Combining like terms we get;

`110-20=5w+4w\\\\90=9w`

Dividing both side by 9 we get;

`(90)/(9)=(9w)/(9)\\\\w=10\ weeks`

Hence Ava and Liam have the same amount of money at 10th week.