Question

You and your brother are saving money to buy a camcorder. You already have

$60 saved and your brother has $45 saved. You plan on saving an additional
$5 each week. Your brother plans on saving an additional $8 each week.
Write and solve an equation to find how many weeks it takes both of you to
save the same amount. Let w represent the number of weeks.

Answer 1

5 weeks.

Explanation:

We have $60, and we're saving an additional $5 each week:

`60+5w`

Our brother has $45, and is saving an additional $8 each week:

`45+8w`

Let's set up an equation:

`60+5w=45+8w`

We had to set these two expressions equal to each other because our end result should be equal.

Subtract
`60` from both sides of the equation:

`5w=-15+8w`

Subtract
`8w` from both sides of the equation:

`-3w=-15`

Divide by the coefficient of
`w`, which is
`-3`:

`w=5`

Check your work:

You can check your work with substitution. Take the initial equation and substitute
`w` with
`5`:

`60+5(5)=45+8(5)`

Simplify:

`85=85`

It checks out!