Finding Equations

Question

This is a story problem and I can't seem to find the right equation to solve this.

 

How much of the aztec coffee, which sells for $6 per pound, and how much of the cinnamon coffee, which sells for $8 per pound, should be mixed to make 5 pounds of the winterfest blend to be sold at $7.20 per pound?

Answer 1

x represents the amount of $8 coffee.

6(5 - x) + 8x = 7.2x

 

Can you solve for x?

Answer 2

1. Set your variables. Let's go with

• A = pounds of aztec coffee and
• C= pounds of cinnamon coffee

 

2. Now make equations using your variables. With 2 unknowns, you'll need 2 equations

• Weight equations: A+C=5
• Cost equation: 6A+8C=7.20(5)

 

3. Now solve! You can use any method you are comfortable with, but I'll use "elimination" because it works well here.

• 6A+6C=30 (I multiplied the entire first equation by 6)
• 6A+8C=36 (just did the math for the second equation, the 7.2*5)
• 2C=6 (subtracted the first equation from the second, to eliminate the variable A
• C=3 (divide by 2)
• Now that I know C=3, I can go back in any equation, but A+C=5 is easiest, and gives us A=2

 

4. Write your answer in response to the question asked:

 

"You should mix 3 pounds of cinnamon coffee with 2 pounds of Aztec coffee."