Question

Thomas has earned $800 and earns $20 every week by mowing lawns. Ken has earned $600 and earns $30 every week for helping his father with household projects. in how many weeks will both Thomas and kens earnings be the same? What will the amount of earnings be?

Answer 1

Hi there!

Let the amount of weeks be represented by X.
Thomas earns $20
every week,
so has a total earning of $20
times the amount of weeks, hence 20X. Now we only need to add the additional $800 to find the correct expression.

`800 + 20x`

Thomas earns $30
every week, so has a total earning of $30
times the amount of weeks, hence 30X. Now we only need to add the additional $600 to find the correct expression.

`600 + 30x`

Now we can set up and solve the expression.

`800 + 20x = 600 + 30x`

Subtract 800 from both sides.

`20x = - 200 + 30x`

Subtract 30x from both sides.

`- 10x = - 200`

Divide both sides by -10.

`x = ( - 200)/( - 10) = 20`

Therefore, in 20 weeks the earnings will be the same. To find the exact amount of earnings we have to plug in x = 20 into one of the expression.

`800 + 20(20) = 800 + 400 = 1200`

Hence, the earnings will be $1200.
~Hope this helps you!