Question

Wolfrich lived in Portugal and Brazil for a total period of 141414 months in order to learn Portuguese. He learned an average of 130130130 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

Wolfrich lived in Brazil for 5 months and 9 months in Portugal

Explanation:

Given;

Total Months = 14

Total Words = 1920

Required

Find the time spent in Portugal and time spent in Brazil

Let P represent Portugal and B represent Brazil; This implies that

`P + B = 14` ---- Equation 1

Considering that he learnt 130 words per month in Portugal and 150 per month in Brazil; This implies that

`130P + 150B = 1920` --- Equation 2

Make P the subject of formula in equation 1

`P = 14 - B`

Substitute 14 - B for P in equation 2

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

Open Bracket

`1820 - 130B + 150B = 1920`

`1820 + 20B = 1920`

Subtract 1820 from both sides

`1820 - 1820 + 20B = 1920 - 1820`

`20B = 100`

Divide both sides by 20

`(20B)/(20) = (100)/(20)`

`B = 5`

Substitute 5 for B in
`P = 14 - B`

`P = 14 - 5`

`P = 9`

Wolfrich lived in Brazil for 5 months and 9 months in Portugal