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?
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!
