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Topic: E homework solutions
July 18, 2019 / By Neal
Question: Thomas wants to add a 60% antifreeze solution to his car radiator. About how much 60% antifreeze solution can he make by mixing 1 gallon of pure antifreeze w/ water? Answer choices: 1 1/2 gallons 1 2/3 gallons 1.6 gallons 0.6 gallons

Kerry | 8 days ago
This appears to be a mixture problem. Now, when solving mixture/solution problems, you consider three things: (i) amount of the mixture, (ii) concentration of the mixture, (iii) amount of the solute. Note that it is conventional to express the concentration as amount of the solute per amount of mixture. This means that if we multiply the amount/volume of the mixture by its concentration, we get the amount of the solute (i.e. antifreeze) in the mixture as shown below: volume of antifreeze solution x concentration of antifreeze solution = volume of pure antifreeze Now we start by writing an equation. If we are given with 1 gallon of pure antifreeze, that would mean that we have 1 gallon of 100% antifreeze. Water on the other hand has 0% antifreeze. Thus the resulting amount of antifreeze would be: (1 gal)(100%) + x(0%) where x = amount of water. Since we're looking for the amount of a 60% antifreeze solution, we equate this expression to another expression for 60% antifreeze and the total volume of the solution: (1 gal)(100%) + x(0%) = (1 + x)(60%) Notice that the volume for the expression on the right is 1 + x is since we add the 1 gallon of pure antifreeze and the x gallons of pure water. Now we can rewrite the equation and solve for x (volume of water): (1 gal)(100%) + x (0%) = (1 + x)(60%) (1)(1) + x(0) = (1+x)(0.6) 1 + 0 = 0.6 + 0.6x 0.4 = 0.6x .: x = 0.667 = 2/3 gallon Thus we know that Thomas would add 2/3 gallons of water to get a 60% antifreeze solution. But recall that since he also adds 1 gallon of pure antifreeze, he has a total of 1 + x = 1 2/3 gallons of 60% antifreeze solution. .: Thomas is able to make 1 2/3 gallons of 60% antifreeze solution. [second choice]
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