A drummer and a guitarist each wrote songs for their band. The guitarist wrote 8 fewer than twice the number of songs that the drummer wrote. They wrote a total of 46 songs.

Group of answer choices

a.g = 2d – 8
g + d = 46

b.d = 2g – 8
d = 46 – g

c.d = 8 ‒ 2g
d + g = 46

1 answer

To solve the problem, we have two variables: let \( d \) represent the number of songs the drummer wrote, and \( g \) represent the number of songs the guitarist wrote.

From the information given, we can form the following equations:

  1. The guitarist wrote 8 fewer than twice the number of songs the drummer wrote: \[ g = 2d - 8 \]

  2. The total number of songs written by both the drummer and guitarist is 46: \[ g + d = 46 \]

Now let's examine the provided answer choices to see which matches our equations.

Option a:

  • \( g = 2d - 8 \)
  • \( g + d = 46 \)

This matches our derived equations.

Option b:

  • \( d = 2g - 8 \) (this is incorrect as per the problem statement regarding the guitarist)
  • \( d = 46 - g \) (this is another equation for total, but not correct with the first part)

Option c:

  • \( d = 8 - 2g \) (this is incorrect as per the information given)
  • \( d + g = 46 \) (this is a correct equation but does not pair with the correct first part)

Based on the analysis:

The correct choice is (a): \[ g = 2d - 8 \] \[ g + d = 46 \]