SOLUTION: A customer has asked a caterer for 60LB of nuts, 60% of which are to be cashews. The caterer has available mixtures of 70% cashews and 45% cashews. How many pounds of each mixture

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Question 32042: A customer has asked a caterer for 60LB of nuts, 60% of which are to be cashews. The caterer has available mixtures of 70% cashews and 45% cashews. How many pounds of each mixture should be used?
Answer by Earlsdon(6294) About Me  (Show Source):
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The caterer needs to mix x lbs of the 70% cashew mixture with (60-x) lbs of the 45% cashew mixture to obtain the 60 lbs of 60% cashew mixture. Change the percentages to their decimal equivalents and write the algebraic equation to solve for x.
x%280.7%29+%2B+%2860-x%29%280.45%29+=+60%280.6%29 Simplify and solve for x.
0.7x+%2B+27+-+0.45x+=+36 Combine like-terms.
0.25x+%2B+27+=+36 Subtract 27 from both sides.
0.25x+=+9 Divide both sides by 0.25
x+=+36
Answer:
The caterer should mix 36 lbs of the 70% cashew mixture with (60-36 = 24) lbs of the 45% cashew mixture to obtain 60 lbs of 60% cashew mixture.