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:
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The guitarist wrote 8 fewer than twice the number of songs the drummer wrote: \[ g = 2d - 8 \]
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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): \[ g = 2d - 8 \] \[ g + d = 46 \]