Question

Brian, Chris, and Damien took a math test that had 20 questions. The number of questions Brian got right is 14 more than 1/4 the number of questions Chris got right. Damien correctly answered 2 less than 5/4 the number of questions Chris answered correctly. If Brian and Damien have the same score, which statement is true?

A. Brian and Damien both answered 2 fewer questions correctly than Chris did.
B. Brian and Damien both answered 4 more questions correctly than Chris did.
C. Brian and Damien both answered 2 more questions correctly than Chris did.
D. Brian and Damien both answered 4 fewer questions correctly than Chris did.

Answer 1

let's let B = # of questions Brian answered correctly, C = the # of questions that Chris answered correctly, D = # of questions Damien answered correctly

The number of questions Brian got right is 14 more than 1/4 the number of questions Chris got right. ---> so B = (1/4)C + 14

Damien correctly answered 2 less than 5/4 the number of questions Chris answered correctly. ---> D = (5/4)C - 2

Brian and Damien got the same score ---> B = D, so you can set Brian and Damien's equations equal to each other.

(1/4)C + 14 = (5/4)C - 2
solve for C. once you have C, you can plug C into either equation to get Brian or Damien's score (since they're the same as each other)