SOLUTION: A bookstore priced all hardback books at $5 a book and all paperbacks at $1. The store sold 30 more paperback books than hardbacks. Total sales were $354. How many types were so

Question 220259: A bookstore priced all hardback books at $5 a book and all paperbacks at $1. The store sold 30 more paperback books than hardbacks. Total sales were $354. How many types were sold?
Answer by likaaka(51) (Show Source): You can put this solution on YOUR website!
You must set up a system of equations. Begin by naming your variables ie.
H is the amount of hardback books sold &
P is the amount of paperback books sold
If the 30 more paperbacks were sold than hardbacks, your first equation is P=30+H
If total sales were $354 and given the costs of each type of book, then 5H+1P=354
Here is your system of equations
P=30+H
5H+P=354
Now substitute the value of P into the second equation to solve
5H+(30+H)=354 **the parenthesis aren't needed here but I used them to illustrate the substitution
Now combine like terms and solve for H
6H+30=354 subtract 30 from both sides
6H+30 -30=354 -30
6H=324 divide 6 from both sides
(6H)/6=324/6
H=54, so 54 hardback books were sold
Given P=30+H, then
P=30+54
P=84, so 84 paperback books were sold
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