To determine how much each person paid, we first need to find the total bill amount, which we can represent as 1 (or the whole bill).
1. **Calculate the contributions of A and B:**
- A paid 1/2 of the bill.
- B paid 1/5 of the bill.
2. **Find their total contributions:**
We add the amounts paid by A and B:
Total paid by A and B = 1/2 + 1/5
3. **Finding a common denominator:**
The least common multiple (LCM) of 2 and 5 is 10. So, we convert the fractions:
1/2 = 5/10 and 1/5 = 2/10
Adding these two gives:
Total paid by A and B = 5/10 + 2/10 = 7/10
4. **Calculate the remaining amount of the bill:**
Now, we subtract the total paid by A and B from the total bill:
Remaining amount = 1 – 7/10 = 3/10
5. **Sharing the remaining bill among C, D, and E:**
This remaining amount of 3/10 will be shared equally by C, D, and E. Since there are 3 people:
Amount paid by each of C, D, and E = (3/10) / 3 = 3/30 = 1/10
6. **Summarizing the contributions:**
- A paid: 1/2
- B paid: 1/5
- C paid: 1/10
- D paid: 1/10
- E paid: 1/10
In conclusion, the fractions of the bill paid by each individual are:
- A: 1/2
- B: 1/5
- C: 1/10
- D: 1/10
- E: 1/10
Thus, the total contributions add up correctly to 1 (or the whole bill).