Mixture problems

Question

a light brew coffee sells for $12.00 per pound is to be mixed with a dark brew coffee that sells for $9.00 per pound to get a 5-pound mixture that will sell for $10.00 per pound. How many pounds of light brew and dark brew coffee should be used?

Answer 1

Let's have l = light coffee and d = dark coffee.

Here's what we know:

l = 5 - d

We have five pounds of the mixture, to the amount of light is 5 pounds minus the pounds of dark coffee.

12l + 9d = 5 * 10

$12 of the light and $9 of the dark each at certain number of pounds is equal to 5 pounds of $10.

 

Since we have a value for l, we can put that into our equation:

12(5 - d) + 9d = 50

60 - 12d + 9d = 50

60 - 3d = 50

-3d = -10

d = 10/3, or 3 ¹/₃ pounds

 

Now that we have a value for d, we can find l:

l = 5 - 10/3

l = 5/1 - 10/3

l = 15/3 - 10/3

l = 5/3 or 1 ²/₃ pounds

 

Let's check our answer:

12 * 5/3 + 9 * 10/3 = 50

60/3 + 90/3 = 50

150/3 = 50

50 = 50