Algebra 1: Linear Equation [word problem] 2?

Question

Suppose you intend to spend $60 buying books. Hardback books cost $12 and paperbackcost $5. How many books of each type can you buy?

Don't only answer, but can you explain it to me, too?

Answer 1

Okay first you need to set up your equation with two variables, X and Y.

X we will set with hard cover
Y will be paperback

if every hardback cost $12 we will use that as the coefficient of X and $5 will be coefficient of Y
that gives us an equation of

12x+5y=60

You must get the variables added together to equal 60.
first you see that if you buy 5 hardcover books you will spend 60 dollars because 5*12=60. By the same logic you could buy 12 paperbacks at 5 dollars each.
5 is a unique number in that every multiple is either 5 or 0. No multiple of 12 can be added to a number ending in a 5 or 0 to equal exactly 60.

so you can buy:

5 hardcover, 0 paperback
0 hardcover, 12 paperback
4 hardcover, 2 paperback
3 hardcover, 4 paperback
2 hardcover, 7 paperback
1 hardcover, 9 paperback

Answer 2

60/12= 5
60/5= 11

Answer 3

four $12 two $5

Answer 4

12x+5y<_60