Question

A test has twenty questions worth 100 points. the test consists of

a. True
b. False questions worth 3 points each and multiple choice questions worth 11 points each. let x represent the
a. True
b. False questions and y represent the multiple choice questions. which system of equations represents this situation?

Answer 1

Using the given information, we know that the variable x represents true/false questions and the variable y represents multiple choice questions. Because there are twenty questions total, this means that the number of multiple choice questions plus the number of true/false questions must equal 20, as shown in the equation below:

x + y = 20

We also were told that true/false questions were were 3 points each and multiple choice questions were worth 11 point each. Each variable represents the number of that type of question, so if we multiply by their respective point values and add the two products together, this should equal the 100 total points on the test, as modeled below:

3x + 11y = 100

Therefore, this makes your system of equations:

x + y = 20

3x + 11y = 100

Hope this helps!