Question

Paulette, Quentin, and Rosie each donated money to a charity. Paulette gave as much money as Quentin and Rosie gave together. If Quentin had given three times more than he gave, he would have given 40$morethanPaulette.AndifRosiehadgiven$20$ less, she would have given half as much as Paulette. How much did Paulette give?

• A. 80$
• B. 120$
• C. 160$
• D. 200$

Answer 1

The correct option is D 200$LettheamountPaulette,QuentinandRosiedonatedbe$ p, q , r $respectively.Given,$ p = q + r $---\left(1\right)$ 3q = p + 40 \Rightarrow q = \dfrac {p + 40}{3} $---\left(2\right)$\Rightarrow r - 20 = \dfrac {p}{2} \Rightarrow r = \dfrac {p}{2} + 20 $---\left(3\right)Substituting\left(2\right)and\left(3\right)in\left(1\right),weget$ p = \dfrac {p + 40}{3} + \dfrac {p}{2} + 20 \Rightarrow p = \dfrac {2p + 80 + 3p + 120}{6} \Rightarrow 6p = 5p + 200 \Rightarrow p = 200 $Thus,Paulettedonated$ $200$.