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The Pérez brothers

The Pérez brothers

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.