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

[[model:questions/solutions/q5476.png]]

William has 55% of X. Father gives $7. He is still short 1/10 = 10% of X.
So he now has 90% of X.

• 55% of X + $\$7$ = 90% of X
• $\$7$ = 35% of X
• 1% of X = $7 \div 35 = \$0.20$
• 100% = X = $0.20 \times 100 = \$20$
• He is still short 10% of X = 0.10 × 20 = $\$2$

Check: Bag $20. William has 55% = $11. + $7 from father = $18. Short by $2 = 1/10 of $20. ✓

Final Answer: 2