Using Equations to Solve Problems

A book shop owner orders some hard-back version costs the shop owner $20 each and the soft-back $12 each. The total order was for 300 books.
When the order arrives there were only 200 books! The shopkeeper wishes to query the order but cannot find his copy of the original order. However his records do tell him that it was going to cost him $5080. How many of each type of the book was his original order for?

Let X : number of hard-back books and Y : number of soft-back books

X + Y = 300
20X + 12Y = 5080

using substitution
20X + 12(300-X) = 5080 solving X gives X = 185

so Y = 115

let h =number of hardback and s = number of softback

h + s = 300
20h + 12s = 5080
20h + 20s = 6000
8s = 920
s = 115
h = 300 - 115 = 185

There are 185 hardback books and 115 softback books.