Let the cost of the bag be \(\$X\).

[[model:questions/solutions/q5477.png]]

William has 55% = \(\frac{11}{20}\) of X.
After father's $7, he is short \(\frac{4}{11}\) of X.
So he now has \(1 - \frac{4}{11} = \frac{7}{11}\) of X.

• \(\frac{11}{20}X + 7 = \frac{7}{11}X\)
• \(7 = \frac{7}{11}X - \frac{11}{20}X\)
• \(7 = \left(\frac{140 - 121}{220}\right)X = \frac{19}{220}X\)
• \(X = 7 \times \frac{220}{19} = \frac{1540}{19} \approx 81.05\)

The cost of the bag is \(\frac{1540}{19}\) dollars.
Final Answer: 1540/19 [NOTE: fraction in question likely garbled; re-verify source]