a butcher has some burger which is 15% fat and some which is 25% fat. how many pounds of each should be mixed to make 60 lb of hamburger which is 18% fat

Question

a butcher has some burger which is 15% fat and some which is 25% fat. how many pounds of each should be mixed to make 60 lb of hamburger which is 18% fat

Answer 1

This is a classic mixture problem. 

 

Let call the number of pounds of 15% fat meat x.

The number of pounds of 25% fat meat must be 60 - x because the total weight of the meat is 60 pounds and

x + (60 - x) = 60

 

The amount of fat in the 15% fat meat is .15x

The amount of fat in the 25% fat meat is .25(60 - x)

We know that when we add these two quantities we must get the total amount of fat in the mixture, which is,

.18 x 60 = 10.8 pounds

 

So, .15x + .25(60 - x) = 10.8

 

Now we simplify and combine like terms.

 

.15x + 15 - .25x = 10.8

-.10x + 15 = 10.8

-.10x = -4.2

x = 42. 

So, we must use 42 pounds of the 15% fat meat.

 

The weight of the 25% fat meat is 60 - x = 60 - 42 = 18 pounds.

 

Hope this helps.  :)

 

Gordon