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?

A book is worth $1 and a DVD is worth $12.

Step-by-step explanation:

The 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 is worth $1).

Now for DVD price, use the second equation:

d=18-6 or d=12 (means that each DVD is worth $12).

A book is worth $1 and a DVD is worth $12.