What's the best deal for you? Systems of Equations

Buying an expensive gadget, computer, or phone?  Doing the math can make you feel better about getting the best deal.  What

An Apple I-Phone 4 costs $400 plus a $20 monthly fee.  A Samsung Galaxy Phone costs $350 plus a $25 monthly fee.  Which phone would be the best deal if both phones required a 12 month contract?

Some students sold popcorn for a fundraising project.  On the first week they sold 6 small bags, and 20 large bags of popcorn, and they took in $31.00 the first week. The second week they sold 12 small bags and 28 large bags of popcorn. Sales totaled $47.00 the second week.  What was the price for a small bag, and what was the price for the large bag of popcorn? 

Step 1: Define the variables

s = small bag

L= large bag

Step 2: Put word problem into equations

6s + 20L = 31

12s + 28L = 47

Step 3: Use algebra to solve for one variable 

2 (6s + 20L = 31)

12s + 28L = 47

Subtract the two equations (simplify expressions) First, Eliminate the variable S

12s + 40L = 62

-12s + 28L = 47 

___________________________  Then, Solve for L

12L = 15

L = 1.25

A large bag costs $1.25

Step 3:  Substitute L = 1.25 and solve for S

6s + 20*(1.25)= 31

6s + 25 = 31

6s = 6

s= 1

Small bags costs $1.00 each

Try your hand at some equation problems at www.khanacademy.org

Level 2: Linear Equations

Level 3: Linear Inequalities