Question

Wolfrich lived in portugal and brazil for a total period of 14 monthsin order to learn portuguese. He learned an average of 130 new words per month when he lived in protugal and an average of 150 new words per month when he lived in brazil. In total he learned 1920 new words. How long did wolfrich live in portugal and how long did he live in brazil?

Answer 1

Wolfrich live in Portugal 9 months and in Brazil 5 months.

Explanation:

Given:

Wolfrich lived in Portugal and Brazil for a total period of 14 months in order to learn Portuguese.

He learned an average of 130 new words per month when he lived in portugal and an average of 150 new words per month when he lived in Brazil.

In total he learned 1920 new words.

Now, to find the months he live in Portugal and in Brazil.

Let the number of months he live in Portugal be
`x.`

And let the number of months he lived in Brazil be
`y.`

So, total number of months:

`x+y=14`

`x=14-y\ \ \ ....(1)`

Now, the total words he learned:

`130x+150y=1920`

Substituting the value of
`x` from equation (1):

`130(14-y)+150y=1920`

`1820-130y+150y=1920`

`1820+20y=1920`

Subtracting both sides by 1820 we get:

`20y=1920-1820`

`20y=100`

Dividing both sides by 20 we get:

`y=5.`

The number of months he lived in Brazil = 5 months.

Now, substituting the value of
`y` in equation (1):

`x=14-y\\\\x=14-5\\\\x=9.`

The number of months he lived in Portugal = 9 months.

Therefore, Wolfrich live in Portugal 9 months and in Brazil 5 months.