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?

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MinahilO56201 MinahilO56201 · Answer 1 · 2022-10-28T09:33:57+02:00

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:

[tex]3.25p-1.75p\ge150[/tex]

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

[tex]\begin{gathered} 3.25p-1.75p\ge150 \\ 1.5p\ge150 \\ \frac{1.5}{1.5}p\ge\frac{150}{1.5} \\ p\ge100 \end{gathered}[/tex]

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.