A fast food restaurant has 25% fat hamburger meat and 15% fat hamburger meat. How many pounds of each type of meat should be mixed to make 90 lb of hamburger meat that is 18% fat?
The mixture will be 90 lb, and contain 18% fat, or 16.2 lbs of fat, leaving 73.8 lbs meat.
So, we can use these two equations, where x represents the amount of 25% meat, and y represents the amount of 15% meat:
.25x + .15y = 16.2
x + y = 90
Taking the second equation, subtract y from both sides:
x = y + 90
Substitute this value for x back into the first equation:
.25(y + 90) + .15y = 16.2
Using distributive property to remove parentheses:
.25y + 22.5 + .15y = 16.2
.1y + 22.5 = 16.2
Subtract 22.5 from both sides:
.1y = 16.2  22.5
.1y = 6.3
Multiply both sides by 10:
y = 63
Plug this value back into the second equation:
x + y = 90
x + 63 = 90
x = 27
So, the mixture should contain 27 pounds of 25%, and 63 pounds of 15%.
Let's check our work:
(27 lbs * .25) + (63 lbs * .15) = 6.75 + 9.45 = 16.2 lbs of fat
The total weight is 90 lbs (27 + 63).
12/19/2013

Kevin F.