**Sub-claim:**A

The students solve problems involving the Major Content with connections to the Standards for Mathematical Practice

Y = Yes; Assessed on Calculator Section

X = Calculator is Specific to Item

N = No; Assessed on Non-Calculator Sections

Z = Calculator Neutral (Could be Calculator or Non-Calculator Sections)

Solve multi-step contextual problems that require writing and analyzing systems of linear inequalities in two variables to find viable solutions.

1. Tasks have hallmarks of modeling as a mathematical practice (less defined tasks, more of the modeling cycle, etc.).

2. Scaffolding in tasks may range from substantial to very little or none.

EOY Released Test Item 21

Practice Test, Unit 1, Item 11 or Paper Test, Unit 1, Item 11

2016 #28

Carson is a high school student with two-part time jobs. He earns $6 per hour for babysitting, and he earns $8 per hour doing clerical work for his father's business. His goal is to earn at least $96 a week, but because of school, he does not want to work more than 15 hours each week.

Let b represent the number of hours Carson works in one week at the babysitting job and let c represent the number of hours Carson works in one week at his father's business. Which inequalities represent the constraints on what Carson can earn and the number of hours he can work in one week? Select all that apply.

a. b + c ≤ 15

b. 6b + 8c ≤ 15

c. 6b + 8c ≥ 15

d. b + c ≥ 96

e. 6b + 8c ≥ 96

f. 6b + 8c ≤ 96

Which combination of numbers of hours would allow Carson to work 15 hours in one week and earn at least $96? Select all that apply.

a. 10 hours babysitting and 5 hours clerical

b. 11 hours babysitting and 4 hours clerical

c. 12 hours babysitting and 3 hours clerical

d. 13 hours babysitting and 2 hours clerical

e. 14 hours babysitting and 1 hour clerical

Suppose Carson worked as a babysitter for 5 hours one week. What is the minimum number of full hours he would need to work at his father's business to earn at least $96 that week?

Enter your answer on the blank.

__________ hours

**Type of items:**Type 1**Color Code:**Peach**Evidence Statement Key:**A-CED.3-1**Calculator:**XY = Yes; Assessed on Calculator Section

X = Calculator is Specific to Item

N = No; Assessed on Non-Calculator Sections

Z = Calculator Neutral (Could be Calculator or Non-Calculator Sections)

**Point**: 1 each (1:26)**Evidence Statement Text:**Solve multi-step contextual problems that require writing and analyzing systems of linear inequalities in two variables to find viable solutions.

**Clarifications, limits, emphases, and other information intended to ensure appropriate variety in tasks:**1. Tasks have hallmarks of modeling as a mathematical practice (less defined tasks, more of the modeling cycle, etc.).

2. Scaffolding in tasks may range from substantial to very little or none.

**Sample Questions (taken from PARCC’s Practice Tests and Released Items):**EOY Released Test Item 21

Practice Test, Unit 1, Item 11 or Paper Test, Unit 1, Item 11

2016 #28

**1. EOY Released Test Item 21**Carson is a high school student with two-part time jobs. He earns $6 per hour for babysitting, and he earns $8 per hour doing clerical work for his father's business. His goal is to earn at least $96 a week, but because of school, he does not want to work more than 15 hours each week.

__PART A:__Let b represent the number of hours Carson works in one week at the babysitting job and let c represent the number of hours Carson works in one week at his father's business. Which inequalities represent the constraints on what Carson can earn and the number of hours he can work in one week? Select all that apply.

a. b + c ≤ 15

b. 6b + 8c ≤ 15

c. 6b + 8c ≥ 15

d. b + c ≥ 96

e. 6b + 8c ≥ 96

f. 6b + 8c ≤ 96

__PART B:__Which combination of numbers of hours would allow Carson to work 15 hours in one week and earn at least $96? Select all that apply.

a. 10 hours babysitting and 5 hours clerical

b. 11 hours babysitting and 4 hours clerical

c. 12 hours babysitting and 3 hours clerical

d. 13 hours babysitting and 2 hours clerical

e. 14 hours babysitting and 1 hour clerical

__PART C:__Suppose Carson worked as a babysitter for 5 hours one week. What is the minimum number of full hours he would need to work at his father's business to earn at least $96 that week?

Enter your answer on the blank.

__________ hours

__PART D:__**Suppose Carson worked as a babysitter for 8 hours one week. What is the minimum number of full hours he would need to babysit that week to earn at least $96 that week?****Enter your answer on the blank. __________ hours**

**2.****Practice Test, Unit 1, Item 11 or****Paper Test, Unit 1, Item 11**
Use the information provided to answer Part A through Part D.

Leah would like to earn to at least $120 per month. She babysits for $5 per hour and works at an ice cream shop for $8 per hour. Leah cannot work more than a total of 20 hours per month. Let x represent the number of hours Leah babysits and let y represent the number of hours Leah works at the ice cream shop.

__PART A:__

Which graph shows the set of points that represents the numbers of hours that Leah can work in order to earn at least $120 and not work more than 20 hours per month?

__PART B:__

Which pairs ( x , y ) represent hours that Leah could work to meet the given conditions? Select all that apply.

a. ( 4 , 15 )

b. ( 5 , 12 )

c. ( 10 , 9 )

d. ( 15 , 5 )

e. ( 19 , 1 )

__
__

__PART C:__

If Leah babysits for 7 hours this month, what is the minimum number of hours she would have to work at the ice cream shop to earn at least $120? Give your answer to the nearest whole hour.

Enter your answer on the blank. ______

__
__

__PART D:__

Leah prefers babysitting over working at the ice cream shop. Out of 20 total hours, what is the maximum number of hours she can babysit to be able to earn at least $120 per month?

Give your answer to the nearest whole hour.

Enter your answer on the blank. ______

**3. 2016 #28**

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 much select two inequalities.

Select two inequalities.

a. 2t + 2.5c ≤ 160

b. 2t + 4c ≤ 160

c. 2t + 4c ≤ 280

d. 2.5t + 3c ≤ 160

e. 4t + 3c ≤ 160

f. 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.

a. 20 tomato and 45 corn

b. 30 tomato and 40 corn

c. 45 tomato and 30 corn

d. 50 tomato and 25 corn

e. 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?

Enter your answer on the blank.

_______ batches of tomato salsa and 20 batches of corn salsa

__PART D:__

The company owner decided 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?

Enter your answer on the blank.

_______ batches of corn salsa

**Answer:**

*To be posted soon*

**Reference:**

PARCC. (n.d.). Retrieved December 20, 2017, from http://www.aps.edu/assessment/parcc