Question

How do I solve this word problem using the substitution method?

Answer 1

Winchester store charges $19 per charm, so if she uses 3 charms, the cost is 19*3, if she uses 5, the cost is 19*5, if she uses "c" charms, the cost of that will be 19*c or 19c.  They also charge a fixed value of 47 bucks for the bracelet to put it on.

Winchester charges in total then   19c + 47



Kim store charges $18 for the charms, so if she uses 3 charms, that'd be 18*3, if she uses 7 charms, that'd be 18*7, if she uses "c" charms, that'd be 18c.  They also charge 48 bucks for the bracelet.

Kim charges in total then 18c + 48.

if the costs "equal" each other, then

$\bf \begin{cases} 19c+47\\ 18c+48 \end{cases}\implies 19c+47=18c+48\implies c=1\\\\ -------------------------------\\\\ \stackrel{\textit{total cost at Winchester}}{19(1)+47}=\stackrel{\textit{total cost at Kim}}{18(1)+48}$