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?

Brian and Damien both answered 2 fewer questions correctly than Chris did
Brian and Damien both answered 4 more questions correctly than Chris did
Brian and Damien both answered 2 more questions correctly than Chris did
Brian and Damien both answered 4 fewer questions

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?


Brian and Damien both answered 2 fewer questions correctly than Chris did
Brian and Damien both answered 4 more questions correctly than Chris did
Brian and Damien both answered 2 more questions correctly than Chris did
Brian and Damien both answered 4 fewer questions

directrix · Answer

B represents the number of questions Brian got right
C represents the number of questions Chris got right
D represents the number of questions Damien got right

directrix · Answer

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

directrix · Answer

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

directrix · Answer

If Brian and Damien have the same score, 

14 + (1/4) * C =  (5/4) C - 2

Solve the equation for C.

directrix · Answer

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