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

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.

To Find:

How long did Wolfrich live in Portugal, and how long did he live in Brazil?

Solution:

Let he lived in Portugal is X and in Brazil is Y month:

Then we know that total period of month is 14 month, we can write in mathematical equation:

X + Y = 14       ...1)

We also know that he learn total new words is 1920, we can also write in mathematical equation:

130 X + 150 Y = 1920       ...2)

Multiply by 150 in equation 1) on both side, we get:

150 X  + 150 Y = 2100      ...3)

Now subtract equation 2) from equation 3), we get:

(150 - 130 ) X = 2100 - 1920

20 X =  180

On solving, we get:

X = 9

Put value of X in equation 1), we get:

X + Y = 14

9 + Y = 14

So:

Y = 5

It means Wolfrich lived in Portugal and Brazil is 9 and 5 moths.