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.
[tex]800 + 20x[/tex]
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.
[tex]600 + 30x[/tex]
Now we can set up and solve the expression.
[tex]800 + 20x = 600 + 30x[/tex]
Subtract 800 from both sides.
[tex]20x = - 200 + 30x[/tex]
Subtract 30x from both sides.
[tex] - 10x = - 200[/tex]
Divide both sides by -10.
[tex]x = \frac{ - 200}{ - 10} = 20[/tex]
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.
[tex]800 + 20(20) = 800 + 400 = 1200[/tex]
Hence, the earnings will be $1200.
~Hope this helps you!
