Question

Mark and Bill each improved their yards by planting hostas and shrubs. They bought their supplies from the same store. Mark spent $60 on 4 hostas and 4 shrubs. Bill spent $150 on 12 hostas and 2 shrubs. What is the cost of one hosta and the cost of one shrub?

Answer 1

• The cost of one hosta is $12; and

,

• The cost of one shrub is $3.

Step-by-step explanation:

Let the cost of one hosta=h

Let the cost of one shrub = s

Mark spent $60 on 4 hostas and 4 shrubs.

`\implies4h+4s=60`

Bill spent $150 on 12 hostas and 2 shrubs.

`\implies12h+2s=150`

Solve the two equations simultaneously.

`\begin{gathered} 4h+4s=60\ldots(1) \\ 12h+2s=150\ldots(2) \end{gathered}`

Multiply equation (1) by 3.

`\begin{gathered} 12h+12s=180\ldots(1b) \\ 12h+2s=150\ldots(2) \\ \text{Subtract} \\ 10s=30 \\ s=(30)/(10) \\ s=\$3 \end{gathered}`

Next, we solve for h.

`\begin{gathered} 12h+2s=150 \\ 12h+2(3)=150 \\ 12h+6=150 \\ 12h=150-6 \\ 12h=144 \\ h=(144)/(12) \\ h=\$12 \end{gathered}`

The cost of one hosta is $12 and the cost of one shrub is $3.