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Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

# A test has 18 problems, which are worth a total of 118 points. ?

There are two types of problems in the test. Each multiple-choice problem is worth 5 points, and each short-answer problem is worth 9 points. how many multiple choice questions does it have and how many short answer questions does it have?

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m + s = 18

5m + 9s = 118

m = 18 – s

5m + 9s = 118

5(18 – s) + 9s = 118

90 – 5s + 9s = 118

4s = 28

s = 7

m = 18 – s = 11

check

5m + 9s = 118

5•11 + 7•9 = 55 + 63 = 118

• Just by inspection the obvious answer is that the 18 is 2 x 9 and 100 is clearly a multiple of 10 and thus 5.

(5 x 20) + (9 x 2) = 118So 2 shorts and 20 multiple choice. The question then becomes looking for other solutions. If we bag the two 9's we already have, then by counting back in 9's from 100 we get 91, 82, 73, 64, 55*, 46, 37, 28, 19, 10*, 1where 55 and 10 are clearly multiples of 5.Giving us two other possible solutions (11 x 5) + (7 x 9)  and (5 x 2) + (9 x 12)

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