Question

Translate to a system.Jake does not want to spend more than $50 on bags of fertilizer and peatmoss for his garden. Fertilizer costs $2 a bag and peat moss costs $5 abag. Jake's van can hold at most 20 bags.

Answer 1

Let x be the number of bags of fertilizer and y be the number of bags of peat moss.

If each bag of fertilizer costs $2, if we buy x bags we will have to pay 2x for it.

If each bag of peat moss costs $5, if we buy y bags we will have to pay 5y for it.

In total, we would have to pay 2x + 5y.

Since Jake does not want to spend more than $50 on them, this sum have to be less than or equal to 50, so we have the first inequality of the system:

`2x+5y\le50`

Also, Jake's van can hold at most 20 bags, so if we buy x bags of fertilizer and y bags of peat moss, we will have a total of x + y bags, and this have to be less than of equal to 20, so we have the second inequality of the system:

`x+y\le20`

Also, we can't buy a negative number of bags of fertilizer or peat moss, so x and y each must be greater than or equal to 0:

`\begin{gathered} x\ge0 \\ y\ge0 \end{gathered}`

So, the system of inequalities is:

`\begin{gathered} x\ge0 \\ y\ge0 \\ x+y\le20 \\ 2x+5y\le50 \end{gathered}`