Question

Sandra has some experienced workers who together build 120 products a week.

She wants to build at least 200 products each week.
To accomplish this, Sandra needs to hire more new workers who can each build 16 products a week.
However, due to space, she can store no more than 300 products each week.
Which of the following are possible numbers of new workers Sandra can hire? Select all that apply.

Answer 1

Sandra can hire 5, 6, 7, 8, 9, 10, or 11 new workers to meet the production target of at least 200 products each week, while considering the storage constraint of no more than 300 products.

Step-by-step explanation:

To solve this problem, we need to determine the number of new workers Sandra can hire in order to meet the production target of at least 200 products each week, while also considering the storage constraint of no more than 300 products each week.

Let's assume the number of new workers Sandra can hire is x. Each new worker can build 16 products per week, so the total number of products built by the new workers is 16x. The experienced workers build 120 products per week, so the total number of products built by all the workers is 120 + 16x.

Given that the total number of products built each week should be at least 200, we can set up the following inequality: 120 + 16x ≥ 200. Solving this inequality, we find that x ≥ 5.

However, we also need to consider the storage constraint. The total number of products cannot exceed 300, so we have the additional inequality: 120 + 16x ≤ 300. Solving this inequality, we find that x ≤ 11.25.

Combining both inequalities, we find that the possible number of new workers Sandra can hire is between 5 and 11. Since the number of workers must be a whole number, the possible numbers of new workers Sandra can hire are 5, 6, 7, 8, 9, 10, and 11.