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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 1920new 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.

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calculista

Let

x ------->the number of months that Wolfrich lived in Portugal

y ------->the number of months that Wolfrich lived in Brazil

we know that

[tex] x+y=14 [/tex]

[tex] x=14-y [/tex] -------> equation [tex] 1 [/tex]

[tex] 130x+150y=1,920 [/tex] -------> equation [tex] 2 [/tex]

Substitute equation [tex] 1 [/tex] in equation [tex] 2 [/tex]

[tex] 130*[14-y]+150y=1920\\ 1,820-130y+150y=1,920\\ 20y=1,920-1,820\\ y=100/20\\ y=5 months[/tex]

Find the value of x

[tex] x=14-y\\ x=14-5 [/tex]

[tex] x=9 months[/tex]

therefore

the answer is

Wolfrich lived in Portugal for [tex] 9 months[/tex]

Wolfrich lived in Brazil for [tex] 5 months[/tex]

Unknown variable are used to find the unknown values of the problem using the algebraic expressions. The Wolfrich lived in Portugal for 9 years and lived in Brazil for 5 years.

The number of years has to be found lives by Wolfrich in Portgal and Brazil.

What is unknown variable?

Unknown variable are used to find the unknown values of the problem using the algebraic expressions.

Given information-

  • Wolfrich lived in Portugal and Brazil for a total period of 14 months to learn Portuguese.
  • The number of average new words learned by the Wolfrich, lived in Portugal is 130.
  • The number of average new words learned by the Wolfrich, lived in Brazil is 150.
  • Total number of word learned by the Wolfrich is 1920.

Suppose Wolfrich lived in Portugal for [tex]x[/tex] years and Wolfrich lived in Brazil for [tex]y[/tex] years.

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

[tex]x+y=14[/tex]

Rewrite equation for [tex]y[/tex],

[tex]y=14-x[/tex]

Suppose the above equation as equation 1,

As total number of word learned by the Wolfrich is 1920 with average 130 words per day in Portugal and 150 words per day in Brazil. thus,

[tex]130x+150y=1920\\[/tex]

Put the value of [tex]y[/tex] from equation 1,

[tex]\begin{aligned}\\130x+150(14-x)&=1920\\130x+2100-150x&=1920\\-20x&=1920-2100\\-20x&=-180\\x&=\dfrac{180}{20} \\x&=9\\\end[/tex]

Hence the Wolfrich lived in Portugal for 9 years.

Put this value in equation 1,

[tex]y=14-x\\y=14-9\\y=5[/tex]

Hence, Wolfrich lived in Brazil for 5 years.

Thus the Wolfrich lived in Portugal for 9 years and lived in Brazil for 5 years.

Learn more about the unknown value here;

https://brainly.com/question/1235185

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