A 12 qrt. cooling system is checked and found to be filled with a solution that is 40 % antifreeze. The desired strength of the solution is 60% antifreeze. how many quarts of solution need to be drained and replaced with pure antifreeze to reach the desired strength.
If q quarts are to be drained, then
.40(12-q) + 1.00q = .60(12)
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To find out how many quarts of solution need to be drained and replaced with pure antifreeze to reach the desired strength, we can use a mixture equation.
Let's start by determining the initial amount of antifreeze in the 12-quart solution with a 40% concentration.
Initial amount of antifreeze = Total volume * Initial concentration
Initial amount of antifreeze = 12 quarts * 40% (in decimal form)
Initial amount of antifreeze = 12 * 0.40
Initial amount of antifreeze = 4.8 quarts
Now, let's set up the mixture equation:
(12 - x) * 0.40 + x * 100% = 12 * 60%,
where x is the number of quarts to be replaced with pure antifreeze.
Simplifying the equation, we have:
4.8 - 0.40x + x = 7.2,
0.60x = 7.2 - 4.8,
0.60x = 2.4.
Now, divide both sides of the equation by 0.60:
x = 2.4 / 0.60,
x = 4.
Therefore, you need to drain and replace 4 quarts of solution with pure antifreeze to reach the desired strength of 60%.