A butcher has some hamburger that is 21% fat and some that is 15% fat. How many pounds of each should be mixed to make 75 lb of hamburger that is 17% fat?

Question

A butcher has some hamburger that is 21% fat and some that is 15% fat. How many pounds of each should be mixed to make 75 lb of hamburger that is 17% fat?

Answer 1

let's denote hamburger meat 1 having 21% fat as h1 with fat content f1 and hamburger meat 2 having 15% fat as h2 with fat content f2

the total amount of hamburger meat is h1 + h2 = 75

the total amount of fat is f1 + f2 = 0.17(75) = 12.75 since we want the total fat to be 17% of the total meat which is 75

f1 = 0.21h1 since it's 21% fat and f2 = 0.15h2 since it's 15% fat

substituting these into the fat equation we get a system of 2 equations in 2 variables:

h1 + h2 = 75

0.21h1 + 0.15h2 = 12.75

we can solve for either h1 or h2 by substitution...

h2 = 75 - h1

0.21h1 + 0.15(75-h1) = 12.75

h1 = 25

therefore h2 = 50

we want to combine 25lbs of 21% fat meat and 50lbs of 15% fat meat.