Question

A butcher is mixing ground turkey breast that is 98% lean and beef that is 90% lean to make a blend that is 92.4% lean. Determine how many pounds of turkey and beef are needed if she wants 100 pounds of the blend.
Follow the steps below:

1. Identify what x and y represent.
2. Write an equation to relate x and y.
3. Write a 2nd equation relating x and y.
4. use either elimination or substitution to solve for x and y.

Could someone also add an explanation on how they solve the problem? These problems always give me a hard time.

Answer 1

See brainly.com/question/8613376 for one way to work mixture problems.

The proportion of beef will be
.. (98 -92.4)/(98 -90) = 5.6/8 = 0.7

70 pounds of beef and 30 pounds of turkey are needed.

_____
1. I would prefer to use "t" and "b" as variables, rather than x and y. That way I can more easilly keep straight that they represent pounds of turkey and pounds of beef, respectively.

2. t + b = 100 . . . . . we want 100 pounds of mix

3. 98%*t +90%*b = 92.4%*100 . . . . . total pounds of lean meat

4. Using subsitution for t, we have
.. 98%*(100 -b) +90%*b = 92.4%*100
.. b*(98 -90) -98*100 = -92.4*100 . . . . . . multiply by -100, collect b terms
.. b = (98 -92.4)*100/(98 -90) . . . . . . . . . add 98*100 and divide by b coefficient
note that this expression is exactly the one we used to write down the answer above.
.. b = 5.6*100/8 = 70 . . . . . . . y, if you like
.. t = 100 -b = 30 . . . . . . . . . . x, if you like

70 pounds of beef and 30 pounds of turkey are needed.