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Section 2.7 Mixture Applications and Uniform Motion 175 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 Step 1: Read the problem. Step 2: Label the unknowns. Classroom Example: p. 179, Exercise 24 Answer 3. 5 gal is needed. Step 3: Write a verbal model. Step 4: Write a mathematical equation. 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. aPure antifreeze from solution 1bapure antifreeze from solution 2ba pure antifreeze in the final solutionb 0.60x 0.10182 0.2018 x2 Step 5: Solve the equation. Subtract 0.2x. Subtract 0.8. Divide by 0.4. Step 6: Interpret the result. 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 Therefore, 2 L of 60% antifreeze solution is necessary to make a final solution that is 20% antifreeze. 3. Applications Involving Uniform Motion The formula (distance) (rate)(time) or simply, d rt, relates the distance traveled to the rate of travel and the time of travel. For example, if a car travels at 60 mph for 3 hr, then d 160 mph213 hours2 180 miles x 2 Example 2 Skill Practice 3. 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?


miller_introductory_algebra_3e_ch1_3
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