Question

Three friends are comparing their weekly paychecks. Donald discovers that he earned one-third of Michael's paycheque, and $80 less than Jacob's paycheque. Together, the three friends earned $2920 in one week. How much did each friend earn?

Answer 1

Answer: Michael's paycheque = $ 1704

Donald's paycheque =  $ 568

Jacob's paycheque = $ 648

Step-by-step explanation:

Let x = Michael's paycheque

Donald's paycheque = $\dfrac13x$

Jacob's paycheque = $\dfrac 13 x+80$

Together, the three friends earned $2920 in one week.

$\Rightarrow\ x+\dfrac13x+\dfrac13 x+80=2920\Rightarrow\ (\dfrac{3+1+1}{3})x=2920-80\\\\\Rightarrow\ \dfrac{5}{3}x=2840\\\\\Rightarrow\ x=2840\times\dfrac{3}{5}\\\\\Rightarrow\ x=1704$

Michael's paycheque = $ 1704

Donald's paycheque = $\dfrac{1704}{3}=\ 568$

Jacob's paycheque = $ 568+80 = $ 648