Question

a women made a deposit of $218. if her deposit consisted of 62 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?​

Answer 1

F = quantity of five dollar bills

S = quantity of single dollar bills

so she deposited 62 bills, that means that whatever F and S are, we know that F + S = 62.

we also know that all those amount to $218, so the fives are really 5*F or 5F from those $218, and the singles are just 1*S of the same $218, so we can also say that 5F + S = 218.

`F+S=62\implies F=62-S \\\\\\ 5F+S=218\implies \stackrel{\textit{substituting from above}}{5(62-S) +S=218}\implies 310-5S+S=218 \\\\\\ 310-4S=218\implies 310=4S+218\implies 92=4S\implies \cfrac{92}{4}=S\implies 23=S`