SOLUTION: 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?

Question 1014530: 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 by Zucchini(70) (Show Source): You can put this solution on YOUR website!
So, set your variables.
Make "d" the cost of the each DVD and "b" the cost of each book.
Now, take your information and write an equation.
David bought 3 DVD's and 4 books, for a total of $40
David: 3d + 4b= 40
Anna bough 1 DVD and 6 books, for a total of $18
Anna: 1d + 6b = 18
Now, this is a system of equations, so put your equations close to each other so you can see them and then solve for either "d" or "b". I'm going to do "d", although it doesn't matter which one you solve for first. I'm going to solve by substitution.
3d + 4b = 40 ; 1d + 6b= 18
1d + 6b = 18 Move the "6b" to the other side:
d= 18 - 6b Now, plug this equation for d in the other equation:
3d + 4b = 40
3(18-6b) + 4b = 40 Now, distribute
54 - 18b + 4b = 40 Collect like terms
-14b = -14 Solve
b = 1, So, each book cost $1, but, we have to find out how much each DVD cost. So, plug in "1" for "b" in Anna's equation:
1d + 6b = 18
1d + 6(1) = 18
1d + 6 = 18
1d = 12
d = 12, So, each DVD cost $12.
Now, to check our work, plug in "12" for "d" in both equations and "1" for "b" and check to see if it works out.
3d + 4b = 40
3(12) + 4(1) = 40
40 = 40 this works
1d + 6b = 18
1(12) + 6(1) = 18
18 = 18 this works also
The answer: The books cost $1 each and the DVD's cost $12 each.
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