Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Review - Exercises - Page 134: 81


y=30 30 lbs of nuts x=20 20 lbs of raisins

Work Step by Step

Raisins: $3.20/lb$ Nuts: $2.40/lb$ Sells 50 lbs of mixture: $2.72/lb$ x=amount of raisins (lbs) y=amount of nuts (lbs) $$x+y=50$$ $$3.2x+2.4y=2.72(50)$$ $$3.2x+2.4y=136$$ Rearrange the original equation to get a value for x or y. $x+y=50$ $x=50-y$ Substitute in the 50-y for x. $$3.2(50-y)+2.4y=136$$ $$160-3.2y+2.4y=136$$ Combine like terms. $$160-0.8y=136$$ Subtract 136 from 160. Then add 0.8y to the right side. $$24=0.8y$$ Divide both sides by 0.8. $$30=y$$ Now substitute y into the equation to find x. $$3.2x+2.4(30)=136$$ $$3.2x+72=136$$ Subtract 72 from 136. $$3.2x=64$$ Divide both sides by 3.2. $$x=20$$
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