BTGModeratorVI wrote: ↑Sat Jun 13, 2020 5:42 am
The average (arithmetic mean) of 3a + 4 and another number is 2a. What is the average of the other number and a ?
A. 2a
B. a - 4
C. a - 2
D. a + 2
E. a + 4
Answer:
C
Source: Kaplan
Let x = the other number
The average (arithmetic mean) of 3a + 4 and another number is 2a.
We can write: [m][fraction](3a + 4) + x/2[/fraction] = 2a[/m]
Multiply both sides of the equation by [m]2[/m] to get : [m]3a + 4 + x = 4a[/m]
Subtract [m]3a[/m] from both sides to get : [m]4 + x = a[/m]
Subtract [m]4[/m] from both sides to get : [m]x = a-4[/m]
What is the average of the other number (x) and [m]a[/m] ?
The average [m]= [fraction]x + a/2[/fraction][/m]
Substitute [m]x[/m] with [m]a-4[/m] to get: average [m]= [fraction](a-4) + a/2[/fraction][/m]
Simplify to get: average [m]= [fraction]2a-4/2[/fraction][/m]
Rewrite this follows: average [m]= [fraction]2(a-2)/2[/fraction][/m]
Simplify to get: average [m]= a-2[/m]
Answer: C
