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.
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.
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.
Part D: To represent the time constraint, we need to write an inequality. Let's assume "x" represents the number of times you can create the product.
The time it takes to create one product is given as 30 minutes. Since you have 200 hours of available time, we can convert this to minutes by multiplying by 60 (since there are 60 minutes in one hour):
200 hours = 200 * 60 minutes = 12,000 minutes
So, the inequality representing the time constraint would be:
30x ≤ 12,000
Part E: To solve the inequality, we can divide both sides of the equation by 30 to solve for "x":
30x ≤ 12,000
x ≤ 12,000 / 30
x ≤ 400
Now let's graph the solution on a number line:
x ≤ 400
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The solution represents that you can create a maximum of 400 products within the 200 hours of available time you have this summer.
To write an inequality representing your time constraint, we need to consider that you have 200 hours available this summer and that it will take you approximately 30 minutes to create your product.
Remember that 1 hour is equivalent to 60 minutes, so 200 hours will be equal to 200 * 60 = 12,000 minutes.
Let's represent the time it will take to create the product as "x" minutes:
x ≤ 12,000
This inequality states that the value of "x" (the time it takes to create the product) should be less than or equal to 12,000 minutes (which represents your available time of 200 hours this summer).
To solve this inequality, there is no need to perform any additional calculations because the inequality is already in its simplest form.
To graph the solution on a number line, draw a horizontal line and mark 12,000 on it. Shade the region to the left of 12,000, including the point itself (since it is less than or equal to). This represents all the possible values of "x" that satisfy the time constraint.
In terms of the situation, the solution x ≤ 12,000 means that as long as the time it takes you to create the product is less than or equal to 12,000 minutes (200 hours), you will be able to complete the product within your available time this summer. If the time required exceeds 12,000 minutes, you will not have enough time to complete the product.