• Register

Welcome to Kemandi Q&A, where you can post problems of Math, Physics, Chemistry and other subjects and receive answers from other members of the community. It is to help high school and college students study and share knowledge.

The use of the site is free.

Need a help on using this site? click here

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?

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

1 Answer

0 votes
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

Rearranging,

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)
...