A meat market has ground beef that is 40% fat and extra lean ground beef that is 15% fat. How many pounds of each(ground beef and extra lean) must be together to get total of 50 pounds of "lean" ground beef that is 25% fat?

To solve this problem, we will use the concept of the weighted average. Let's assume we need x pounds of ground beef and y pounds of extra lean ground beef.

Step 1: Set up the equation for the total weight:
x + y = 50

Step 2: Set up the equation for the fat content:
(0.4x + 0.15y)/(x + y) = 0.25

Step 3: Simplify the equation for the fat content:
0.4x + 0.15y = 0.25(x + y)

Step 4: Solve the system of equations:
0.4x + 0.15y = 0.25x + 0.25y
0.15y - 0.25y = 0.25x - 0.4x
-0.1y = -0.15x
y = -0.15x / -0.1
y = 1.5x

Substitute the value of y in terms of x into the total weight equation:
x + 1.5x = 50
2.5x = 50
x = 50 / 2.5
x = 20

Substitute the value of x back into y = 1.5x:
y = 1.5 * 20
y = 30

Therefore, you need 20 pounds of ground beef and 30 pounds of extra lean ground beef to get a total of 50 pounds of "lean" ground beef that is 25% fat.

To solve this problem, we can set up a system of equations based on the information given.

Let's assume x represents the number of pounds of ground beef, and y represents the number of pounds of extra lean ground beef.

We know that the total weight of the lean ground beef is 50 pounds:
x + y = 50 -- Equation 1

We also know that the fat content in ground beef is 40%:
0.4x -- Equation 2

And the fat content in extra lean ground beef is 15%:
0.15y -- Equation 3

The total fat content in the 50 pounds of lean ground beef is 25%:
0.25(50) -- Equation 4

Now, we can set up the equation based on the fat content:
0.4x + 0.15y = 0.25(50)

Simplifying the equation, we have:
0.4x + 0.15y = 12.5

Now, we can solve the system of equations by using substitution or elimination.

Using substitution, we can solve Equation 1 for y:
y = 50 - x

Substituting the value of y in Equation 2:
0.4x + 0.15(50 - x) = 12.5

Simplifying the equation:
0.4x + 7.5 - 0.15x = 12.5
0.25x + 7.5 = 12.5
0.25x = 5
x = 20

Substituting the value of x in Equation 1 to find y:
20 + y = 50
y = 30

Therefore, you would need 20 pounds of ground beef and 30 pounds of extra lean ground beef to get a total of 50 pounds of lean ground beef that is 25% fat.

amount of the 40% beef --- x

amount to the 15% beef --- 50-x

solve for x

.4x + .15(50-x) = .25(50)
I would multiply each term by 100

40x + 15(50-x) = 25(50)
etc