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:
Option C
Brian and Damien both answered 2 more questions correctly than Chris did
Solution:
Let "x" be the number of correct answers of Brian
Let "y" be the number of correct answers of Chris
Let "z" be the number of correct answers of Damien
The number of questions Brian got right is 14 more than 1/4 the number of questions Chris got right
[tex]x = 14 + \frac{1}{4}y\\[/tex] ---------- eqn 1
Damien correctly answered 2 less than 5/4 the number of questions Chris answered correctly
[tex]z = \frac{5}{4}y - 2[/tex] ---------- eqn 2
Brian and Damien have the same score
x = z -------- eqn 3
Therefore,
[tex]14 + \frac{1}{4}y = \frac{5}{4}y - 2\\\\\frac{5}{4}y - \frac{1}{4}y = 14+2\\\\y = 16[/tex]
Substitute y = 16 in eqn 1
[tex]x = 14 + \frac{16}{4}\\\\x = 14 + 4\\\\x = 18[/tex]
Therefore, by eqn 3,
z = 18
Thus we get,
Number of correct answers of Brian = 18
Number of correct answers of chris = 16
Number of correct answers of Damien = 18
Therefore, correct statement is:
Brian and Damien both answered 2 more questions correctly than Chris did
Answer:
Brian and Damien both answered 2 more questions correctly than Chris did.-B
Step-by-step explanation:
