Question

Un local de Santa Bárbara fue pintado por 4 personas emprendedoras que se unieron para montar un negocio de lácteos; Juan, Pedro, Carlos y Mario; Juan pintó 2/7 del local, Pedro pintó 5/14 y Carlos pintó 2/14; ¿qué fracción pintó Mario?

Answer 1

The proportion of premises painted by Mario is
`(3)/(14)`.

Explanation:

The question is:

A local in Santa Bárbara was painted by 4 enterprising people who got together to start a dairy business; Juan, Pedro, Carlos and Mario; Juan painted 2/7 of the premises, Pedro painted 5/14 and Carlos painted 2/14; What fraction did Mario paint?

Solution:

Consider the proportion of the total premises painted is 1.

The four enterprising people who got together to start a dairy business are:

Juan (J), Pedro (P), Carlos (C) and Mario (M).

The proportion of premises painted by Juan is:

`P(J)=(2)/(7)`

The proportion of premises painted by Pedro is:

`P(P)=(5)/(14)`

The proportion of premises painted by Carlos is:

`P(C)=(2)/(14)`

Compute the proportion of premises painted by Mario as follows:

P (M) = 1 - P (J) - P (P) - P (C)

`=1-(2)/(7)-(5)/(14)-(2)/(14)\\=(14-4-5-2)/(14)\\=(3)/(14)`

Thus, the proportion of premises painted by Mario is
`(3)/(14)`.