A test has 20 questions worth 100 points. The test consists of true/false questions worth 3 points each and multiple choice questions 11 points each. How many multiple choice questions are on the test

Question

Graph your equations.

Answer 1

Let x = number of true/false questions, y = number of multiple choice.

x + y = 20 (total number of questions is 20)

3x + 11y = 100 (each true false is 3 points, each mult choice is 11 and total points is 100)

Substitution method is probably easier than addition/elimination, so solve the first equation for y and substitute into the 2nd.

y = 20 -x

3x + 11(20 - x) = 100

3x + 220 -11x = 100

220 - 8x -= 100

120 = 8x

x = 120/8 = 15

y = 20 - 15 = 5 (this is the number of multiple choice questions)

Check:

3(15) + 11(5) =? 100

45 + 55 ?= 100

100 = 100 check