A necklace broke while two lovers were playing.

A row of pearls escaped:

the sixth part to the ground fell;

the fifth part in the bed stayed;

a third, for the young woman was saved;

the tenth part the well loved picked up,

and with six pearls the cord stayed.

Tell me reader, **How many pearls did the necklace of the blessed have?**

#### Solution

We can solve the problem through an equation. We call * x* to the total number of pearls in the necklace. According to the problem, we would have:

x = x / 6 + x / 5 + x / 3 + x / 10 + 6

We look for the m.c.m. of 6,5,3 and 10 m.c.m. = 30 and we rewrite the equation:

x = 5x / 30 + 6x / 30 + 10x / 30 + 3x / 30 + 6

x = 24x / 30 + 6

We multiply by 30 both sides of the equation:

30x = 24x + 180

30x - 24x = 180

6x = 180

x = 180/6

x = 30

Thus, **the necklace of the blessed had 30 pearls**.