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.

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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.