Question

1. In a group of 100 persons, 72

people can speak Visayan and 43
can speak Chavacano. How many
can speak Visayan only? How many
can speak Chavacano only and how
many can speak both Visayan and
Chavacano?

Answer 1

First how many are speaking both. We know that 72+43=115 which is more than the total.

115-100=15 that is the number of people that speak both.

The number of Visayan speakers who also speak Chavacano is x, the number of Chavacano speakers who also speak Visayan is y.

`x+y=15`

The number of people who speak only 1 language is 85. For Visayan only speakers,

`v=72-x`

For Chavacano only speakers,

`c=43-y`

where
`v+c=85`.

So we have,

`v=72-x`

`c=43-(15-x)=43-15+x=28+x`

Add the equations up,

`v+c=28-x`

`85=28+x\implies\boxed{x=57}`

Repeat with y,

`v=72-(15-y)=57+y`

`c=43-y`

Add them up,

`v+c=100\implies 85=100`

which means there are no solutions because we do not have sufficient information.

Hope this helps :)