Question

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.
How long did Wolfrich live in Portugal and how long did he live in Brazil?
Wolfrich lived in Portugal for (?) months and lived in Brazil for (?) months

Answer 1

We let...

x as the number of months he spent in Portugal

y as the number of months he spend in Brazil

From the problem, we can generate the following equations

x + y = 14

130x + 150y = 1920

Solving the equation gives us

x = 9 months in Portugal

y = 5 months in Brazil

Answer 2

Answer: He lived in Portugal for 9 months and in Brazil for 5 months.

Explanation:

Let the number of months he lived in Portugal be 'x'.

Let the number of months he lived in Brazil be 'y'.

Total number of months = 14

Average new words per month when he lived in Portugal = 130

New words in x months = 130x

Average new words per month when he lived in Brazil = 150

New words in y months = 150y

Total new words = 1920

So, our equation would be

`x+y=14-------(1)\\\\130x+150y=1920-------------(2)`

Let x = 14-y from equation 91).

Now, we put this value in equation (2).

`130(14-y)+150y=1920\\\\1820-130y+150y=1920\\\\1820+20y=1920\\\\20y=1920-1820\\\\20y=100\\\\y=5`

if y = 5

then, x= 14-5 = 9

Hence, he lived in Portugal for 9 months and in Brazil for 5 months.