Question

Write and solve an inequality for each of the word problems.You start growing geraniums from seed and plan to sell potted plants at a farm stand. It costs you $1.75 to pot and grow each plant. If you sell each plant for $3.25, how many plants will you need to sell if you want to make a profit of at least $150?

Answer 1

We can answer this question if we remember that the profit is the difference between the amount earned and the amount we spent.

Then we have the following:

1. Let p be the number of plants.

2. The amount spent per plant is $1.75.

3. The amount we will sell the plant will be $3.25 per plant.

4. Since we need to earn at least $150, we have to represent this having into account that it means that we need to earn $150 or more (>=).

Now, we can represent the situation as follows:

`3.25p-1.75p\ge150`

Since we have only one variable, p, in the inequality, we can add algebraically the coefficients as follows:

`\begin{gathered} 3.25p-1.75p\ge150 \\ 1.5p\ge150 \\ (1.5)/(1.5)p\ge(150)/(1.5) \\ p\ge100 \end{gathered}`

Therefore, we have to sell, at least, 100 plants to make a profit of at least $150. If we sell more than 100 plants, we will earn more than $150.