Scott wants to make 6 gal of a 50% sugar solution by mixing together a 60% sugar solution and pure water. How much of each solution must he use?

Question

mixture 1 @ 60% = x gallons
pure water = 100% - x (??? that's my question...is that correct? or is it 0?)
mixture @ 50% = 6 gallons

60x + 100(6-x)= 50 * 6
60x + 600-100x = 300
600 - 40x = 300
-40x = -300
x = 7.5

Answer 1

I would do it this way:
Amount of pure water needed --- x gal
Amount of the 60% stuff ------ 6-x

.6(6-x) + 0x= .5(6)
3.6 - .6x = 3
-.6x = -.6
x = 1

so use 5 gal of the 60% plus 1 gal of pure water

your answer of 7.5 gal should have made no sense to you. You want to end up with only 6 gal, so how could you add 7.5 ????

Answer 2

Thank you. My answer of 7.5 didn't make sense. i was obviously overthinking...thinking pure would = 100%.
Again, thanks for your help.