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A Math quiz has 25 questions. A correct answer earns 8 points, and a wrong one costs 3 points. Jess scores 110 points. How many questions does Jess answer?

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asked Oct 22, 2015 in K-12 by w1002 (660 points)

1 Answer

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Let r be the number of right answers, w the number of wrong answers

8r - 3w = 110

8r - 80 = 3w + 30, 8(r-10) = 3(w+10)

x-10 must be a multiple of 3, and y+10 must be a multiple of 8. Use "k" as a positive constant.

x-10 = 3k, y+10 = 8k


r = 10+3k

w = -10+8k

Add these two and get

x+y = 11k

Because there are 25 questions,

x+y <= 25, so k must be 1 or 2. However, if y is to be positive (which it must), k >1. K must equal 2

Plug into x+y=11k, and x+y = 22.

Jess answered 22 questions.
answered Oct 28, 2015 by 32fun (6,320 points)