Antonio, Begoña, Carlos and Diana have had a snack at the bar. When paying, they do it equally. Once the account is paid, they prove that although everyone has paid the same, Antonio has put 10% of the money he had, Begoña 20%, Carlos 30% and Diana 40%.

If we know that at the beginning they all had a whole number of euros (without cents),

**How much money did each initially have at least?**

#### Solution

If we identify each person with the initial of his name Antonio (**to**), Begoña (**b**), Charles (**c**) and Diana (**d**),

with the data they give us, we have to 10% **to** = 20% **b** = 30% **c** = 40% **d**.

Or what would be the same, 0'1**to** = 0'2**b** = 0'3**c** = 0'4**d**.

If we put them in function of **to**, we have to **to** = 2**b** = 3**c** = 4**d**.

As they tell us that at the beginning all of them had an integer number of euros, we calculate the least common multiple of the 4 numbers (1,2,3,4), which is 12. And therefore, we know that **to**, has 12 euros, which **b**, which has half, has 6 euros, **c**, the third part, 4 euros, and **d**, the fourth part, 3 euros. So everyone paid 1.2 euros.