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Question Number 40057 by Rio Mike last updated on 15/Jul/18

Mike and Stev had 620 bucks  each to spend . Mike used all  his money to buy 3pens and   4books,while Stev bought   4pens and 3books and had a  balance of 50 bucks.Find  the cost of a pen and book.

$${Mike}\:{and}\:{Stev}\:{had}\:\mathrm{620}\:{bucks} \\ $$$${each}\:{to}\:{spend}\:.\:{Mike}\:{used}\:{all} \\ $$$${his}\:{money}\:{to}\:{buy}\:\mathrm{3}{pens}\:{and}\: \\ $$$$\mathrm{4}{books},{while}\:{Stev}\:{bought}\: \\ $$$$\mathrm{4}{pens}\:{and}\:\mathrm{3}{books}\:{and}\:{had}\:{a} \\ $$$${balance}\:{of}\:\mathrm{50}\:{bucks}.{Find} \\ $$$${the}\:{cost}\:{of}\:{a}\:{pen}\:{and}\:{book}. \\ $$$$ \\ $$

Answered by MJS last updated on 16/Jul/18

3p+4b=620 ⇒ p=((620−4b)/3)  4p+3b=570 ⇒ p=((570−3b)/4)  4(620−4b)=3(570−3b)  2480−16b=1710−9b  770=7b  b=110  p=((620−440)/3)=60

$$\mathrm{3}{p}+\mathrm{4}{b}=\mathrm{620}\:\Rightarrow\:{p}=\frac{\mathrm{620}−\mathrm{4}{b}}{\mathrm{3}} \\ $$$$\mathrm{4}{p}+\mathrm{3}{b}=\mathrm{570}\:\Rightarrow\:{p}=\frac{\mathrm{570}−\mathrm{3}{b}}{\mathrm{4}} \\ $$$$\mathrm{4}\left(\mathrm{620}−\mathrm{4}{b}\right)=\mathrm{3}\left(\mathrm{570}−\mathrm{3}{b}\right) \\ $$$$\mathrm{2480}−\mathrm{16}{b}=\mathrm{1710}−\mathrm{9}{b} \\ $$$$\mathrm{770}=\mathrm{7}{b} \\ $$$${b}=\mathrm{110} \\ $$$${p}=\frac{\mathrm{620}−\mathrm{440}}{\mathrm{3}}=\mathrm{60} \\ $$

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