Question Number 40057 by Rio Mike last updated on 15/Jul/18
$${Mike}\:{and}\:{Stev}\:{had}\:\mathrm{620}\:{bucks} \\ $$$${each}\:{to}\:{spend}\:.\:{Mike}\:{used}\:{all} \\ $$$${his}\:{money}\:{to}\:{buy}\:\mathrm{3}{pens}\:{and}\: \\ $$$$\mathrm{4}{books},{while}\:{Stev}\:{bought}\: \\ $$$$\mathrm{4}{pens}\:{and}\:\mathrm{3}{books}\:{and}\:{had}\:{a} \\ $$$${balance}\:{of}\:\mathrm{50}\:{bucks}.{Find} \\ $$$${the}\:{cost}\:{of}\:{a}\:{pen}\:{and}\:{book}. \\ $$$$ \\ $$
Answered by MJS last updated on 16/Jul/18
$$\mathrm{3}{p}+\mathrm{4}{b}=\mathrm{620}\:\Rightarrow\:{p}=\frac{\mathrm{620}−\mathrm{4}{b}}{\mathrm{3}} \\ $$$$\mathrm{4}{p}+\mathrm{3}{b}=\mathrm{570}\:\Rightarrow\:{p}=\frac{\mathrm{570}−\mathrm{3}{b}}{\mathrm{4}} \\ $$$$\mathrm{4}\left(\mathrm{620}−\mathrm{4}{b}\right)=\mathrm{3}\left(\mathrm{570}−\mathrm{3}{b}\right) \\ $$$$\mathrm{2480}−\mathrm{16}{b}=\mathrm{1710}−\mathrm{9}{b} \\ $$$$\mathrm{770}=\mathrm{7}{b} \\ $$$${b}=\mathrm{110} \\ $$$${p}=\frac{\mathrm{620}−\mathrm{440}}{\mathrm{3}}=\mathrm{60} \\ $$