158 Chapter 2 Linear Equations and Inequalities 2. Applications Involving Mixtures Solving a Mixture Application How many liters (L) of a 60% antifreeze solution must be added to 8 L of a 10% antifreeze solution to produce a 20% antifreeze solution? Solution: The information can be organized in a table. Notice that an algebraic equation is derived from the second row of the table. This relates the number of liters of pure antifreeze in each container. The amount of pure antifreeze in the final solution equals the sum of the amounts of antifreeze in the first two solutions. Step 5: Solve the equation. Subtract 0.2x. Subtract 0.8. Divide by 0.4. Step 6: Interpret the result. pure antifreeze from solution 2 0.60x 0.10182 0.2018 x2 0.60x 0.10182 0.2018 x2 0.6x 0.8 1.6 0.2x 0.6x 0.2x 0.8 1.6 0.2x 0.2x 0.4x 0.8 1.6 0.4x 0.8 0.8 1.6 0.8 0.4x 0.8 0.4x 0.4 0.8 0.4 x 2 Therefore, 2 L of 60% antifreeze solution is necessary to make a final solution that is 20% antifreeze. Skill Practice 2. How many gallons of a 5% bleach solution must be added to 10 gallons (gal) of a 20% bleach solution to produce a solution that is 15% bleach? a Pure antifreeze from solution 1 b a b a pure antifreeze in the final solution b Example 2 Step 1: Read the problem. Step 2: Label the variables. Answer 2. 5 gal is needed. Step 3: Write a verbal model. Step 4: Write a mathematical equation. 60% 10% Final Mixture: Antifreeze Antifreeze 20% Antifreeze Number of liters of solution x 8 18 x2 Number of liters of pure antifreeze 0.60x 0.10182 0.2018 x2
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