Lesson Word problems on mixtures for dry substances like candies, dried fruits
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<H2>Word problems on mixtures for dry substances like candies, dried fruits</H2> <H3>Problem 1</H3>Ellen wishes to mix candy worth $1.90 per pound with candy worth $3.50 per pound to form 32 pounds of a mixture worth $2.80 per pound. How many pounds of the more expensive candy should she use? <B>Solution</B> Let x be an amount of candies worth $1.90 per pound Ellen uses to mix, in pounds. The amount of candies worth $3.50 per pound in the mix is 32-x pounds. The total value of candies in the mix is 1.9x+3.5(32-x) dollars. At the price of the mix of $2.80 per pound it gives an equation {{{(1.9*x + 3.5*(32-x))/32}}} = {{{2.80}}}. Simplify and solve it: 1.9*x + 3.5*(32-x) = 2.80*32. 1.9x + 112 - 3.5x = 89.6, -1.6x = -22.4 x = 14. 32-14 = 18. <B>Answer</B>. 14 pounds at $1.90 and 18 pounds at $3.50 should be used. <H3>Problem 2</H3>The Sweet Shoppe wishes to sell a mixture of chocolate covered pretzels & macadamia nuts. The pretzels worth $3 per pound and the nuts worth $8 per pound. How many pounds of the nuts should be mixed with 50 pounds of the pretzels to make a mixture that would sell for $6 for pound? <B>Solution</B> Let <B>x</B> be an amount of nuts to mix in pounds. Then the value of nuts is 8x dollars. The value of pretzels is 3*50 dollars. The balance equation is Value of nuts + Value of pretzels = value of mixture, or 8x + 3*50 = 6(x+50). Simplify and solve it: 8x + 150 = 6x + 300, 2x = 150, x= 75. <B>Answer</B>. 75 pounds of nuts should be added to the pretzels. <H3>Problem 3</H3>Joanne makes a mixture of dried fruits by mixing dried apples costing $6.00 per kilogram and dried apricots costing $8.00 per kilogram. How many kilograms of each are needed to make 20 kilograms of a mixture worth $7.20 per kilogram? <B>Solution</B> Let <B>x</B> be an amount of dried apples to be mixed, in pounds. Then the required amount of dried apricots is 20-x pounds. The value of the dried apples is 6*x dollars; the value of the dried apricots is 8*(2-x) dollars. The price of the mix should be $7.20. It gives an equation {{{(6x+8(20-x))/20}}} = {{{7.20}}} Simplify and solve it: 6x + 160 - 8x = 7.20*20, -2x = -160 + 144, -2x = -16, x = 8. 20 - x = 20 - 8 = 12. <B>Answer</B>. 8 kilograms of dried apples at $6 per kilogram and 12 kilograms of apricots at $8 should be mixed. 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