Hello, I know how to solve a problem like this, but I cannotfigure out the equat

Question

Hello, I know how to solve a problem like this, but I cannotfigure out the equation. I will show you what I put as theequation, but I am pretty sure it is wrong. The title of thechapter is Systems of Equations. "Arctic Antifreeze" is 18% alcohol and "Frost-No-More" is 10%alcohol. How many liters of Arctic Antifreeze should be mixed with7.5L of Frost-No-More in order to get a mixture that is 15%alcohol? My Equation: A + B = 7.5 .18A + .10B = .15 Let A= Amount of Arctic Antifreeze Let B= Amount of Frost-No-More Any help or guesse would be greatly appreciated, thank you allso much for taking the time to read/help answer my question. ~ Summer :) Hello, I know how to solve a problem like this, but I cannotfigure out the equation. I will show you what I put as theequation, but I am pretty sure it is wrong. The title of thechapter is Systems of Equations. "Arctic Antifreeze" is 18% alcohol and "Frost-No-More" is 10%alcohol. How many liters of Arctic Antifreeze should be mixed with7.5L of Frost-No-More in order to get a mixture that is 15%alcohol? My Equation: A + B = 7.5 .18A + .10B = .15 Let A= Amount of Arctic Antifreeze Let B= Amount of Frost-No-More Any help or guesse would be greatly appreciated, thank you allso much for taking the time to read/help answer my question. ~ Summer :)

Explanation / Answer

First, you're starting with 7.5L of Frost-No-More and adding to itx liters of Arctic Antifreeze, so after you're done mixing, you'llhave 7.5 + x Liters of solution. To find out the concentrations, you have 7.5 Liters of 10% solutionand you're adding x Liters of 18% solution. When you're done,you'll have (7.5 + x) liters of a 15% solution. Thus, yourequation is... (0.10)(7.5) + (0.18)(x) = (0.15)(7.5 + x) 0.75 + 0.18x = 1.125 + 0.15x 0.03x = 0.375 x = 12.5 So, you need to add 12.5 liters of Arctic Antifreeze. =========== If you want to set it up as a system of equations (it's a bitoverkill for this particular question, but you can do it) Let A = Liters of Arctic Antifreeze Let B = Liters of Frost-No-More Then A + B = 7.5 + B 0.10A + 0.18B = 0.15(A+B) From the first equation you have that A = 7.5, plug that into the2nd equation 0.10(7.5) + 0.18(B) = 0.15(7.5+B) Which is the same equation we got above. B = 12.5

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