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Topic: **E homework solutions****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

May 22, 2019 / By Neal

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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1. Solving this problem may not help you learn anything. 2. Learning how to solve this problem is more important than getting the right answer. 3. Not sure what an sid is, but yes, you look at the number in front of the variable, since you want that side of the equation to only have a variable left on it, the other side of the equation has the answer at the end... What you are supposed to be learning here includes the fact that you can do the same thing to both sides of an equation without changing the answer! So, in this case, we must divide each side by 12.8 so that the variable Y is left all alone on the left side...see solution below. However, you aren't thinking about the problem, or your solution, with any depth. Another way to approach the problem is just substitute a number in the variable and see what happens. In that way you can see what a "reasonable" solution might look, so that you can judge when you are finished whether you are close or not. Put a 1 in for the variable just to see what you get. 12.8*1 = 12.8 So you know that isn't the answer. However, the answer is, as you figured out, half of something! Try 1/2 or .5 and substitute the variable - now you see the answer anyway... 12.8y=6.4 12.8y/12.8 = 6.4/12.8 y = .50

Can you clarify? I'm not sure what you're asking... But if you divide 12.8 by 6.4 and get 2, that means that 6.4 times 2 is 12.8. You had that backwards. If you need to find Y, then you need to divide both sides by 12.8 to get y=(6.4/12.8). Hope that helped.

Since the answer is equal to 6.4, you should try dividing the answer (6.4), by the one factor that you do know (12.8), to get the answer for y. basically, 12.8 multiplied by y equals 6.4. So 6.4 divided by 12.8 should give you y. Make sense?

Lol ^. Yellow fever killed alot of people...more emphasis on suitable living environments? How did the Constitution shape us? What? It is the document that documents (lol) our rights, our freedoms, who we are as a nation...

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