Question

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

Answer 1

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)**:
\[
g = 2d - 8
\]
\[
g + d = 46
\]