A test has twenty questions worth 90 points. The test consists of True/False questions worth 2 points each and multiple choice questions worth 9 points each. Ho

Question

Please show me complete solutions. A test has twenty questions worth 90 points. The test consists of True/False questions worth 2 points each and multiple choice questions worth 9 points each. How many multiple choice questions are on the test? (Note : As much as possible round off to whole number)

Answer 1

Let T = # of true false questions

let M = # of multiple choice

then

T + M = 20

and 

2T + 9M = 90

so solve system of 2 equations and 2 unknowns

one way is to multiply first equation by 2

2T + 2M = 40

and subtract second equation

-7M = -50

M = 7 1/7 or 7 when rounded

from the first equation

T = 20 - M = 13

 

The question should have been posed as total score = 89; then no rounding would have required and the answer would have been exact.