A butcher wishes

Question

A butcher wishes to sell ground beef that is 80% lean (20% fat,) She currently has 40 pounds of 90% lean ground beef on hand and some beef lard. How many pounds of beef lard should she add to the existing 90% mixture to end up with the desired 80% lean ground beef?

Answer 1

Looking at it from the perspective of the amount of fat:

10% of 40# = 4#'s of fat in the 90% lean meat. x = amt of lard to add (100% fat)

80% lean target will have 20% fat by wt. After adding lard, will have 40 + x lbs of ground beef.

4 + x = 0.2(40 + x)

4 + x = 8 + 0.2x

-4 = -0.8x → x = 5 lbs of lard

Or, 0.8 = 0.9(40)/(x + 40)

0.8 = 36/(x + 40)

0.8(x + 40) = 36

0.8x + 32 = 36

0.8x = 4 → x = 4/0.8 = 5 lbs.

Answer 2

Hello John,

From the given information, we can see some equation. In fact, to solve this kind of math problem, one key step is to discover the equation. In the given process, to mix the 40 pounds 90% lean ground beef into the 80% lean ground beef, what will stay the same?

The problem states that “She currently has 40 pounds of 90% lean ground beef on hand and some beef lard.” The problem then asks, “How many pounds of beef lard should she add to …..”. Both pieces of info suggest that the amount of lard will be changing, while the amount of the lean part stays the same before and after the mix. Hence, we found a way to build up our equation, keep the amount of lean part the same before and after the mix.

Before the mix, the amount of lean from the 40 pounds of 90% beef is 40*90%.

After the mix, this amount stays the same. However, we have a different way to express this amount. The connection is with the end product of mix, i.e. the 80% beef.

The lean part for the 80% beef is (40 + lard) * 80%.

Our equation is then, 40*90% = (40+lard)*80%. Solve for lard.