262 Chapter 3 Systems of Linear Equations and Inequalities 2. Applications Involving Mixtures Solving an Application Involving Chemistry Example 2 One brand of cleaner used to etch concrete is 25% acid. A stronger industrialstrength cleaner is 50% acid. How many gallons of each cleaner should be mixed to produce 20 gal of a 40% acid solution? Solution: Let x represent the amount of 25% acid cleaner. Let y represent the amount of 50% acid cleaner. 25% Acid 50% Acid 40% Acid Number of gallons of solution x y 20 Number of gallons of pure acid 0.25x 0.50y 0.40(20), or 8 From the first row of the table, we have a Amount of 25% solution b a amount of 50% solution b atotal amount From the second row of the table we have Amount of pure acid in 25% solution amount of pure acid in 50% solution of solution amount of pure acid in b x y 20 ° ¢ ° ¢ ° 0.25x0.50y8 resulting solution x y 20 x y 20 0.25x 0.50y 8 2 5x 50y 800 Multiply by 25. ¢ x y 20 25x 25y 500 25x 50y 800 25x 50y 800 x y 20 x 1122 20 x 8 25y 300 y 12 Multiply by 100 to clear decimals. Create opposite coefficients of x. Add the equations to eliminate x. Substitute back into one of the original equations. y 12 Therefore, 8 gal of 25% acid solution must be added to 12 gal of 50% acid solution to create 20 gal of a 40% acid solution. Skill Practice 2. A pharmacist needs 8 ounces (oz) of a solution that is 50% saline. How many ounces of 60% saline solution and 20% saline solution must be mixed to obtain the mixture needed? Avoiding Mistakes Do not forget to write the percent as a decimal. Answer 2. The pharmacist should mix 6 oz of 60% solution and 2 oz of 20% solution. TIP: A word problem can be checked by verifying that the solution meets the conditions specified in the problem. 5 hot dogs 1 drink 5($4.00) 1($2.00) $22.00 ✔ 2 hot dogs 3 drinks 2($4.00) 3($2.00) $14.00 ✔
miller_intermediate_algebra_4e_ch1_3
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