SOLUTION: A butcher decides to mix hamburger so it can be sold at a competitive price. If he mixes some that is 22% fat with some that is 10% fat, how many pounds of each type should he mix

Algebra ->  Linear-equations -> SOLUTION: A butcher decides to mix hamburger so it can be sold at a competitive price. If he mixes some that is 22% fat with some that is 10% fat, how many pounds of each type should he mix       Log On


   

Question 1121434: A butcher decides to mix hamburger so it can be sold at a competitive price. If he mixes some that is 22% fat with some that is 10% fat, how many pounds of each type should he mix to get 80 pounds of hamburger that is 16% fat?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Notice 16% is exactly in the middle of 22% and 10%.

40 pounds of each.


------
Algebra steps were requested.

x, the pounds of 22% fat hamberger
80-x, the pounds of the 10% fat hamberger

Quantity of mix wanted was given 80 pounds of 16% fat.

Account for the amount of fat.
highlight_green%2822x%2B10%2880-x%29=80%2A16%29, keeping as percents on both sides of equation instead of decimal fractions;

22x%2B800-10x=80%2A16
12x=80%2A16-800
12x=480
highlight%28x=40%29---------which is obviously half of the total mix of 80 pounds. 40 pounds of the 22% fat hamburger.

80-40=highlight%2840%29--------pounds of the 10% fat hamburger.