To determine the maximum number of songs that can be purchased for Company A to be a better buy than Company B, we need to set up an inequality comparing the total costs of each company.
Let \( x \) be the number of songs purchased.
Cost for Company A:
Company A charges $1.25 per song, so the cost for \( x \) songs is:
\[
\text{Cost}_A = 1.25x
\]
Cost for Company B:
Company B charges a one-time membership fee of $4 plus $0.65 per song, so the total cost for \( x \) songs is:
\[
\text{Cost}_B = 4 + 0.65x
\]
We need to find the largest \( x \) for which Company A is a better buy than Company B: \[ 1.25x < 4 + 0.65x \]
Let's solve this inequality step by step:
-
Subtract \( 0.65x \) from both sides: \[ 1.25x - 0.65x < 4 \] \[ 0.60x < 4 \]
-
Divide both sides by \( 0.60 \): \[ x < \frac{4}{0.60} \] \[ x < \frac{40}{6} \] \[ x < \frac{20}{3} \] \[ x < 6.67 \]
Since \( x \) has to be a whole number, the maximum integer value for \( x \) is \( 6 \).
Therefore, the maximum number of songs that can be purchased for Company A to be a better buy is 6.