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158 Chapter 2 Linear Equations and Inequalities in One Variable 0.25(40) + 0.60(x) = 0.30(40 + x) 10 + 0.60x = 12 + 0.30x 10 + 0.60x - 0.30x = 12 + 0.30x - 0.30x 10 + 0.30x = 12 10 + 0.30x - 10 = 12 - 10 0.30x = 2 0.30x = 0.30 2 0.30 x = 20 3 or 6 2 3 Louisa needs to add 6 2 3 Express the relationship. Simplify. Subtract 0.30x from each side. Simplify. Subtract 10 from each side. Simplify. Divide each side by 0.30. Simplify. mL of the 60% copper sulfate solution to the 40 mL of 25% copper sulfate solution to obtain a 30% copper sulfate solution. 3c. A specialty coffee shop wants to make an After Dinner Blend from two of their coffees, French Roast and Java. The French Roast sells for $14 per pound and Java sells for $8 per pound. How many pounds of French Roast should be mixed with 10 lb of Java to produce an After Dinner Blend that sells for $12 per pound? Solution 3c. What is unknown? The pounds of French Roast are unknown. Let x = pounds of French Roast. What is known? French Roast sells for $14 per pound, Java sells for $8 per pound, and the blend sells for $12 per pound. There are 10 lb of Java. Type of Coffee Pounds of coffee × Price per pound = Total price of coffee French Roast x $14 14x Java 10 $ 8 8(10) After Dinner Blend x + 10 $12 12(x + 10) The combined price of the French Roast and Java equals the total price of the After Dinner Blend. This gives us the following equation. 14x + 8(10) = 12(x + 10) 14x + 80 = 12x + 120 14x + 80 - 12x = 12x + 120 - 12x 2x + 80 = 120 2x + 80 - 80 = 120 - 80 2x = 40 2x 2 = 40 2 Express the relationship. Simplify and distribute. Subtract 12x from each side. Simplify. Subtract 80 from each side. Simplify. Divide each side by 2. x = 20 Simplify. To make the blend, 20 lb of French Roast should be mixed with 10 lb of Java. Student Check 3 Write an equation that can be used to solve each problem. Solve the equation and answer the question using a complete sentence. a. Damien has a collection of nickels and dimes. He has twice as many dimes as nickels. The value of his collection is $5.25. Find the number of nickels and dimes in his collection.


hendricks_beginning_algebra_1e_ch1_3
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