A mixture of lean ground beef with 2% fat is mixed with fatty ground beef with 10% fat to create a ground beef mix with 8% fat. What is the ratio of lean ground to to fatty ground beef in the new mixture?
Fat percentage in the lean beef: 2%.
Fat percentage in the fatty beef: 10%.
Fat percentage in the mixture: 8%.
Let L = the lean beef and F = the fatty beef.
The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.
Step 1: Plot the 3 percentages on a number line, with the percentages for L and F on the ends and the percentage for the mixture in the middle.
L 2%-------------8%-----------10% F
Step 2: Calculate the distances between the percentages.
L 2%------
6-----8%-----
2------10% F
Step 3: Determine the ratio in the mixture.
The required ratio of L to F is the RECIPROCAL of the distances in red.
L:F = 2:6 = 1:3.
Additional problem:
How many pounds of fatty beef are needed to form 24 pounds of mixture?
Since L:F = 1:3, of every 4 pounds of mixture, 1 pound is L and 3 pounds are F.
Thus, in 24 pounds of mixture, F = (3/4) * 24 = 18 pounds.
For two similar problems, check here:
https://www.beatthegmat.com/ratios-fract ... 15365.htmlPrivate tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
