Coffee mixtures?

Question

A coffee company wants a new flavor of cajun coffee. How many pounds of coffee worth $10.00 a pound should be added to 30 pounds of coffee worth $3.00 a pound to get a mixture worth $6.00 a pound?

Answer 1

Let x = the number of pounds we need of the $10 coffee and m = the mixed amount

Here's what we know:

10x + 3 * 30 = 6m (x pounds of $10 coffee and 30 pounds of $3 make m pounds of $6)

m = a + 30 (the amount of mixed is the $3 and $10 pounds together)

 

Since we have a value for m, lets put that into our equation:

10x + 90 = 6(x + 30)

Distribute:

10x + 90 = 6x + 180

Constants to one side:

10x = 6x + 90

Variables to the other:

4x = 90

Isolate x by dividing by 4

x = 22.5 pounds

 

Check:

10 * 22.5 + 3 * 30 = 6(22.5 + 30)

225 + 90 = 6 * 52.5

315 = 315