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

let us say hmm

p = months in Portugal

b = months in Brazil

Wolfrich learned 130 words in portugal, every month, so if he lived there 1 month, he got 130*p or 130*1 or 130 words only

two months, 130*2 or 260 words

three months 130*3 or 390 words and so on

so... if he lived only "p" months, he learned then, 130 * p, or 130p

in Brazil, he learned 150 monthly, same as before, if he lived "b" months, then he learned 150 * b, or 150b

he spent a total of 14 months on both places

so.. .whatever "b" is, and whatever "p" is, we know that

b + p = 14

and he learned a total of 1920 words

so... whatever 150b is, and whatever 130p is, we know that

150b + 130p = 1920

therefore

$\bf \begin{cases} b+p=14\implies \boxed{p}=14-b\\ 150b+130p=1920\\[-0.5em] \hrulefill\\ 150b+130\left( \boxed{14-b} \right)=1920 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 150b+1820-130b=1920\implies 20b=100\implies b=\cfrac{100}{20}\implies \blacktriangleright b=5 \blacktriangleleft \\\\\\ p=14-b\implies \blacktriangleright p=9 \blacktriangleleft$

Answer 2

Answer: P= 9 months

B=5 months

Step-by-step explanation: