Question

6. In the summer, Paul earns twice as much each week painting rooms than he does cuttinggrass. His total weekly wages are $150 more than that of his younger sister, Megan, whobabysits. She earns one quarter as much as Paul does painting rooms. How much doesPaul earn from each of his jobs?

Answer 1

Paul earns $60 for cutting grass.

Paul earns $120 for painting rooms.

Explanation:

Let x be the money Paul earns cutting grass.

We can establish the following equation with the help of the statement:

`\begin{gathered} \text{Paul, painting rooms = 2x} \\ \text{Megan babysitting = 1/4 }\cdot\text{ 2x} \\ \text{therefore:} \\ \text{ painting rooms + cutting grass = \$150 + babysitting } \\ \text{ replacing:} \\ 2x+x=150+(1)/(4)2x \\ 3x=150+(1)/(2)x \\ 3x-(1)/(2)x=150 \\ (5)/(2)x=150 \\ x=(2)/(5)\cdot150 \\ x=60 \\ \text{then,} \\ \text{Paul, cutting grass = \$60} \\ \text{Paul, painting rooms = \$120} \end{gathered}`