Algebra 1 PARCC: a little salsa

The following multi-part question, explained here in hopes of helping algebra students in Maryland and Illinois prepare for the PARCC test near the end of this school year, appears on the released version of PARCC’s Spring 2016 test in algebra 1 (#28), here:

Spicy bean tortillas with corn salsa and avocado

A local salsa company makes two types of salsa, tomato and corn. Each batch of tomato salsa takes 2 hours to prepare and 4 hours to package. Each batch of corn salsa takes 2.5 hours to prepare and 3 hours to package. There are 4 preparation workers and 7 packaging workers in the company. Each of them works 40 hours per week.

Part A

Create a system of two inequalities that relates the number of batches of tomato salsa, t, and the number of batches of corn salsa, c, that can be made by the 4 preparation workers and the 7 packaging workers each week. Assume t > 0 and c > 0. You must select two inequalities.

  1. 2t + 2.5c < 160
  2. 2t + 4c < 160
  3. 2t + 4c < 280
  4. 2.5t + 3c < 160
  5. 4t + 3c < 160
  6. 4t + 3c < 280

Part B

Which combinations of batches of salsa could be made in one week based on the constraints?

Select all that apply.

  1. 20 tomato and 45 corn
  2. 30 tomato and 40 corn
  3. 45 tomato and 30 corn
  4. 50 tomato and 25 corn
  5. 60 tomato and 10 corn

Part C

In order to maximize productivity, how many batches of salsa should be made if the company owner wants 20 batches of corn salsa?

Part D

The company owner decides to only make corn salsa one week prior to a local festival. Given the same constraints, what is the maximum number of batches of corn salsa that can be made in one week?

Answer and references
Example of a solution strategy (there are others)

Analysis of this question and online accessibility

The question measures knowledge of the Common Core standard it purports to measure and tests students’ ability model a real-world system using systems of two equations or inequalities in two unknowns. It is considered to have a median cognitive demand.

The question can be tested online and should yield results that are as valid and reliable as those obtained on paper. In addition, no special accommodation challenges can be identified with this question, so the question is considered fair.

About the Author

Paul Katula
Paul Katula is the executive editor of the Voxitatis Research Foundation, which publishes this blog. For more information, see the About page.

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