Atest has thirty questions worth 100 points. the test consists of true/false questions worth 3 points each and multiple choice questions worth 8 points each. how many multiple choice questions are on the test?

The number of true/false questions is ' T '.
They're worth 3 points each, so the total true/false points is 3T .

The number of multiple choice is ' M '.
They're worth 8 points each, so the total multiple choice points is 8M .

T + M = 30 questions all together
3T + 8M = 100 points all together

Multiply each side of the first equation by 8,
and write the second equation under it:

8T + 8M = 240
3T + 8M = 100

Subtract the second equation from the first one:  5T = 140

Divide each side by  5  :  T = 28 t/f questions

The rest of the 30 questions are multiple choice . . .
only 2 multiple choice questions.

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