




Massachusetts Comprehensive Assessment System
2014, Grade 10 Mathematics
Question 36: OpenResponse 

Reporting Category: Algebra and Functions Standard: 10.P.8  Solve everyday problems that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution. Use technology when appropriate. Include mixture, rate, and work problems. (AI.P.12)
Standard: Mathematics.A.REI.3.06  Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 
A chef is making 20 pounds of fruit salad to sell in his shop. The chef will use only grapes and blueberries in the fruit salad.
Let x and y be defined as follows: x = the number of pounds of grapes the chef will use
 y = the number of pounds of blueberries the chef will use
 Write an equation in terms of x and y that can be used to represent the total number of pounds of fruit salad the chef will make.
Grapes cost $2.50 per pound, and blueberries cost $4.00 per pound. The chef spent a total of $59.00 for grapes and blueberries for the fruit salad. Write an equation in terms of x and y that can be used to represent the total cost, in dollars, of the fruit salad.
 Use your answers from parts (a) and (b) to determine the number of pounds of grapes and the number of pounds of blueberries the chef will use to make the fruit salad. Show or explain how you got your answer.

Scoring Guide and Sample Student Work Select a score point in the table below to view the sample student response.
Score  Description 
4 
The student response demonstrates an exemplary understanding of the Algebra and Functions concepts involved in solving systems of linear equations exactly, focusing on pairs of linear equations in two variables. The student models a given situation with two equations and solves the system of equations algebraically. 
4 
3 
The student response demonstrates a good understanding of the Algebra and Functions concepts involved in solving systems of linear equations exactly, focusing on pairs of linear equations in two variables. Although there is significant evidence that the student was able to recognize and apply the concepts involved, some aspect of the response is flawed. As a result the response merits 3 points. 
2 
The student response demonstrates a fair understanding of the Algebra and Functions concepts involved in solving systems of linear equations exactly, focusing on pairs of linear equations in two variables. While some aspects of the task are completed correctly, others are not. The mixed evidence provided by the student merits 2 points. 
1 
The student response demonstrates a minimal understanding of the Algebra and Functions concepts involved in solving systems of linear equations exactly, focusing on pairs of linear equations in two variables. 
0 
The student response contains insufficient evidence of an understanding of the Algebra and Functions concepts involved in solving systems of linear equations exactly, focusing on pairs of linear equations in two variables to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 10 Mathematics
 Question 17: Number and Quantity
 Question 20: Geometry
 Question 21: Statistics and Probability
 Question 36: Algebra and Functions
 Question 41: Geometry
 Question 42: Algebra and Functions
Return to the MCAS 2014 Student Work Directory
Last Updated: September 27, 2017


