Part D. The amount of time it will take me to create my product will be 30 minutes. I have 200 hours this summer to devote to creating your product. Write an inequality that represents my time constraint.

Question

Part E. Solve the inequality from part D and graph the solution on a number line. Explain what the solution means in terms of the situation.

Answer 1

Part D:
Let "x" be the number of times I can create my product this summer.
Since it takes me 30 minutes to create one product, the total time it will take me to create "x" products is 30x minutes.
We have that there are 200 hours in the summer. As there are 60 minutes in an hour, that is 12000 minutes.
Therefore, the inequality representing my time constraint is:
30x ≤ 12000.

Part E:
To solve the inequality 30x ≤ 12000, we divide both sides by 30:
x ≤ 400.

We can graph the solution on a number line by marking a closed circle at 400, and shading to the left of it.

In terms of the situation, the solution x ≤ 400 means that I can create a maximum of 400 products this summer within my time constraint of having 200 hours to devote to creating the product.