Thinking process:
- Samy had 4/5 of what Tim had. So we can suppose Samy had 4 units.
- Samy used 1/3 of his money. So perhaps it is better to use 3 x 4 units.

Working:
        Samy     Tim
Start    12u     15u
Food      4u     10u
Remain            5u     

 4u: Since Samy spent 1/3 of 12u to pay for food.
10u: Since 4u is 2/7 of food cost, so it cost 14u. Tim paid 10u.
 5u: That means 5u = $10 and u = $2.

The meal cost 14u = $28.