A butcher has some hamburger that is 18% fat and some that is 12% fat. How many pounds of each should be mixed to make 81 lb of hamburger that is 14% fat?

Question

How many pounds of 18% fat and how many pounds of 12% fat? Requires two answers

Answer 1

These problems require solving a set of equations.   

 

Let X = lbs of 18% burger needed

Let Y = lbs of 12% burger needed

 

So X + Y = 81

 

Now consider the total amount of fat that will be combined.  This must equal the total fat in the final mixture.

 

0.18X + 0.12Y = 0.14 * 81

 

I would solve these by using the elimination method.   So multiply the first equation by .18 to obtain

 

.18X + ,18Y = 81 *.18

.18X + .12Y = 81 *.14

 

Subtracting the two yields

 

,06Y = 81 *.04

 

Y = 81 * .04/.06 = 54 lbs of 12 % fat burger

 

Since X+Y = 81, then  X = 27 lbs of 18% fat burger