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?

Answer 1

Answer: he lived 9 months in Portugal and 5 months in Brazil.

Step-by-step explanation:

Let x represent the number of months he lived in Portugal.

Let y represent the number of months he lived in Brazil.

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

x + y = 14

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. This means that

130x + 150y = 1920- - - - - - - - - - - 1

Substituting x = 14 - y into equation 1, it becomes

130(14 - y) + 150y = 1920

1820 - 130y + 150y = 1920

- 130y + 150y = 1920 - 1820

20y = 100

y = 100/20

y = 5

x = 14 - y = 14 - 5

x = 9