Modeling with Matrices — Quiz

Question 1 • Advanced Algebra: Concepts and Connections

A test is worth 100 points. The test is made up of 40 items. Each item is worth either 2 points or 3 points. Which matrix equation and solution represent the situation?

Answer

the 2 by 3 matrix row 1, 1 1 40 row 2, 2 3 100 There are 20 items worth 2 points each and 20 items worth 3 points each.

the 2 by 3 matrix row 1, 1 1 40 row 2, 2 3 100 There are 10 items worth 2 points each and 30 items worth 3 points each.

the 2 by 3 matrix row 1, 1 2 40 row 2, 1 3 100 There are 10 items worth 2 points each and 30 items worth 3 points each.

the 2 by 3 matrix row 1, 1 2 40 row 2, 1 3 100 There are 20 items worth 2 points each and 20 items worth 3 points each.

Explanation

Let x be the number of 2-point items and y the number of 3-point items. The situation gives x + y = 40 and 2x + 3y = 100, matching the matrix in choice A. Doubling the first equation gives 2x + 2y = 80; subtracting it from the points equation gives y = 20, so x = 20. Thus there are 20 items of each kind, as choice A states.

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