Algebra

A mixture of 12% disinfectant solution is to be made from 10% and 17% disinfectant solution. how much of each solution should be used if 14 gallons of the 12% solution are needed?

I don't think the question is quite complete.

I will assume for starters that you have lots of the 17% solution and you can make it all up from that.

There is a really simple formula for this

Amount of strong concentrate needed = concentration wanted / concentration availble * amount that you want to make up

Amount of strong concentrate needed = 12% / 17% * 14gallons (the percent signs can just be cancelled out)
= 12/17*14
= 9.88 g (to 2 dec places)
Then you will have to add (14-9.88) 4.12 gallons of water.

If you use the 10% mixture you will have to add some of the 17% mixture as well or it won't be strong enough.

A lovely morning here in Adelaide. Thought I'd try my hand at this to see if it can be done without adding water, just mixing the 10 and 17's together. Bit hungover. Hmmmm.
14 gallons of 12%. Lets multiply them together and forget about the percentages for the moment....
14x12+168. We want 168 by mixing 10a plus 17b where a and b are the gallons we are trying to work out.
We can solve a and b by remembering that a plus b = 14 gallons, so
a = 14-b
So, Lets put it all together....
168=10(14-b) +17b
168=140 -10b+17b
Simplify
28 = 7b
b=4 gallons, thats the strong stuff, and
a=10 gallons of the weak stuff.
Lets check if correct.
10x10 + 17x4=168
Yipee!!!!!!!
Cheers