EXAMPLE 4 Solve a mixture problem ANTIFREEZE

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EXAMPLE 4 Solve a mixture problem ANTIFREEZE For extremely cold temperatures, an automobile manufacturer recommends that a 70% antifreeze and 30% water mix be used in the cooling system of a car. How many quarts of pure (100%) antifreeze and a 50% antifreeze and 50% water mix should be combined to make 11 quarts of a 70% antifreeze and 30% water mix?

EXAMPLE 4 Solve a mixture problem SOLUTION STEP 1 Write an equation for the total number of quarts and an equation for the number of quarts of antifreeze. Let x be the number of quarts of 100% antifreeze, and let y be the number of quarts of a 50% antifreeze and 50% water mix.

EXAMPLE 4 Solve a mixture problem Equation 1: Total number of quarts x + y = 11 Equation 2: Number of quarts of antifreeze x quarts of 100% antifreeze y quarts of 50%–50% mix 11 quarts of 70%–30% mix 1 x + 0.5 y = 0.7(11) x + 0.5y = 7.7

Solve a mixture problem EXAMPLE 4 Solve a mixture problem The system of equations is: x + y =11 Equation 1 x + 0.5y = 7.7 Equation 2 STEP 2 Solve Equation 1 for x. x + y = 11 Write Equation 1 x = 11 – y Revised Equation 1 STEP 3 Substitute 11 – y for x in Equation 2 and solve for y. x + 0.5y = 7.7 Write Equation 2.

Solve a mixture problem EXAMPLE 4 Solve a mixture problem (11 – y) + 0.5y = 7.7 Substitute 11 – y for x. Solve for y. y = 6.6 STEP 4 Substitute 6.6 for y in the revised Equation 1 to find the value of x. x = 11 – y = 11 – 6.6 = 4.4 ANSWER Mix 4.4 quarts of 100% antifreeze and 6.6 quarts of a 50% antifreeze and 50% water mix to get 11 quarts of a 70% antifreeze and 30% water mix.

GUIDED PRACTICE for Example 4 WHAT IF? How many quarts of 100% antifreeze and a 50% antifreeze and 50% water mix should be combined to make 16 quarts of a 70% antifreeze and 30% water mix? 6. ANSWER 6.4 quarts of 100% antifreeze and 9.6 quarts of a 50% antifreeze and 50% water mix