Problem (Algebra):
Paul was planning to buy 20 items from the ARML shop. He wanted some mugs, which cost $\$ 10$ each, and some shirts, which cost $\$ 6$ each. After checking his wallet he decided to put $40 \%$ of the mugs back. Compute the number of dollars he spent on the remaining items.

Solution:
The problem does not state the number of mugs Paul intended to buy, but the actual number is irrelevant. Suppose Paul plans to buy $M$ mugs and $20-M$ shirts. The total cost is $10 M+6(20-M)$ However, he puts back $40 \%$ of the mugs, so he ends up spending $10(0.6 M)+$ $6(20-M)=6 M+120-6 M=\mathbf{1 2 0}$ dollars.

Final answer: 120