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?

1 Answer
Apr 19, 2017

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.