Question

David bought 3 DVDs and 4 books for $40 at a yard sale. Anna bought 1 DVD and 6 books for $18. How much did each DVD and book cost?

Answer 1

A book is 12 times cheaper than a DVD

Explanation:

Your equations (2 unknowns and two equations, d is for a DVD and b is for a book):
For David: `3d+4b=40`
For Anna: `d+6b=18`

Now multiply the second equation with -3 and add to the first equation:

`3d+4b=40`
`-3d-18b=-54`
Combined equation: `-14b=-14` and `b=1` (means that each book worths $1).

Now for DVD price, use the second equation:
`d=18-6` or `d=12` (means that each DVD worths $12).

A book worths $1 and a DVD worths $12.