10.A test has twenty questions worth 100points. The test consists of True/Falsequestions worth 3 points each and multiplechoice questions worth 11 points each. Thissystem of equations can be used to find howmuch of each question type the test has.payt in,uldthex + y = 203x + 11y = 100Where x represents the number of true/falsequestions, and y represents the number ofmultiple choice questions. The solution tothe system is (15, 5). What is the correctinterpretation of this solution?m:

Answered: 10. A test has twenty questions worth…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Step 1

Consider the system of given linear equations.

$x + y = 20 . . . . . . . (1) 3 x + 11 y = 100 . . . . . . . (2)$

Let x represents the number of true/false questions, and y represents the number of multiple choice questions.

Solve the above equations as follows.

$(1) \times 3 \Rightarrow 3 x + 3 y = 60 (2) \Rightarrow 3 x + 11 y = 100 (-) - 8 y = - 40 \Rightarrow 8 y = 40 \Rightarrow y = \frac{40}{8} \Rightarrow y = 5$

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