Mr. Pérez has five most active children:

- On Monday they go to the cinema FOUR of them whose ages add up to 38 years.
- On Tuesday, FOUR children whose ages total 35 years go out to skate.
- On Wednesday they go to the FOUR children's amusement park. Adding their ages we are 36 years old.
- FOUR of the children go out to the pool on Thursday and their ages add up to 36.
- FOUR of the children go to a concert on Friday and their ages add up to 38.
- On Saturday they go to FOUR children's football and this time their ages add up to 39.

If none of the boys went out every day, **What is the age of each?**.

#### Solution

In total we have 24 departures, that is, 6 days multiplied by 4 children at each departure. This means that one of the children will leave 4 days and the other four will leave 5 days. If we call **to**, **b**, **c**, **d** Y **and** at the ages of each of the children we have to:

4a + 5b + 5c + 5d + 5e = 222

From this expression we can deduce the following:

4a + 4 b + 4c + 4d + 4e + b + c + d + e = 222

and therefore:

4 (a + b + c + d + e) + b + c + d + e = 222

From here we deduce that a + b + c + d + e = 46 and that b + c + d + e = 38 of this second formula we deduce that **a = 8** and from the first we get that a + c + d + e = 36 and therefore **b = 10**.

We can also deduce that a + b + c + e = 39 and therefore **d = 7**.

It is fulfilled that a + b + c + d = 36 and then **e = 10**.

And finally a + b + e + d = 35 where we get that **c = 11**.

Thus, the ages of the children are: **a = 8 years, b = 10 years, c = 11 years, d = 7 years and e = 10 years**.