The cooling system of Alex's car holds 10 quarts. It is now filled with a mixture that is 60% water and 40% antifreeze. Hearing a weather forecast for severe cold, Alex decides to increase the strenth of the antifreeze mixture to 50%. To do this, Alex must drain off a certain number of quarts from the cooling system and then replace them by pure antifreeze. How many quarts must be drained?
+37146 Alex needs 10 quarts of 50% ....so he needs 5 quarts of antifreeze and 5 qts water
he currently has only 4 quarts antifreeze and 6 quarts of water
....a 40% solution
.40 (x) + 1 (10-x) = .50 (10)
.40x + 10 -x = 5
-.6x = -5
x = 5/.6 = 8.333 quarts of 40% will be needed to start then 1.67 quarts of pure antifreeze will be added
10 - 8.33 = 1.67 quarts to drain and refill with 100% a-freeze
+37146 Alex needs 10 quarts of 50% ....so he needs 5 quarts of antifreeze and 5 qts water
he currently has only 4 quarts antifreeze and 6 quarts of water
....a 40% solution
.40 (x) + 1 (10-x) = .50 (10)
.40x + 10 -x = 5
-.6x = -5
x = 5/.6 = 8.333 quarts of 40% will be needed to start then 1.67 quarts of pure antifreeze will be added
10 - 8.33 = 1.67 quarts to drain and refill with 100% a-freeze
