SOLUTION: How many gallons of a 60% antifreeze solution must be mixed with 70 gallons of 25% antifreeze to get a mixture that is 50% antifreeze? I don't have the first clue on how to figu

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Question 530337: How many gallons of a 60% antifreeze solution must be mixed with 70 gallons of 25% antifreeze to get a mixture that is 50% antifreeze?
I don't have the first clue on how to figure this out. Can you please explain this process?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the required number of gallons of the 60% antifreeze solution.
You can represent the amount of antifreeze in the solution as follows:
Change the percentages to their decimal equivalents: 60% = 0.6, 25% = 0.25, and 50% = 0.5
For example, the amount of antifreeze in 70 gallons of 25% antifreeze solution = 0.25(70) = 17.5 gallons.
0.6x+0.25(70) = 0.5(70+x) Simplify.
0.6x+17.5 = 35+0.5x Subtract 0.5x from both sides.
0.1x+17.5 = 35 Subtract 17.5 from both sides.
0.1x = 17.5 Divide by 0.1
x = 175 gallons