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?
Answers
Answer:
Step-by-step explanation:
Let's lay out all the information we have:
Math test = 20 questions
Brian = B
Chris = C
Damien = D
B = 14 + (1/4)C
D = 2 - (5/4)C
B=D
From this, we can see that Brian and Damien are supposed to have the same score. Thus, we make each equation equal to each other.
14 + (1/4)C = 2 - (5/4)C
Now, we can add +(5/4) from each side so that we only have 1 C value in our equation.
14 + (1/4)C + (5/4)C = 2 - (5/4)C + (5/4)C
14 + (6/4)C = 2
We can now simplify the fraction and move 14 to the other side of the equation.
14 - 14 + (6/4)C = 2 - 14
(6/4)C = -12
6 and 4 can both be divided by 2 giving:
(3/2)C = -12
3/2 is equal to 1.5 and so we can now divide -12 by 1.5
(3/2)C = -12
1.5C = -12
1.5C/1.5 = -12/1.5
C = -8
From this answer we can calculate the number of correct answers Brian and Damien each had on the test.
B = 14 + (1/4)C
B = 14 + (1/4)(-8) --> we can divide -8 by 4 giving -2
B = 14 + (-2)
B = 12
D = 2 - (5/4)C
D = 2 - (5/4)(-8) --> we can again divide -8 by 4 = -2, and then multiply -2 by 5 giving -10
D = 2 - (-10)
D = 2 + 10
D = 12
So, we can conclude that Brian and Damien do have the same score.
Answer:A
Step-by-step explanation: