Question

how many gallons of 70% antifreeze should be mixed with 10 gallons of 30% antifreeze to obtain a 45% antifreeze mixture

Answer 1

I have a special way of solving these equations: You take the two percentages and subtract the smaller one from the larger one, in this case 40%. Now find the difference between the specified percentage and the two given percentages:
70%-45%=25%
45%-30%=15%
Now you see that 25% is 5/8 of 40%, and 15% is 3/8 of 40%. Now flip these completely over between the antifreezes.

70%-45%=25% give this one 15% (3/8)
45%-30%=15% give this one 25% (5/8)

Now you see that the 70% mixture will be 3/8 of your final mixture and the 30% mixture will be 5/8 of the final mixture. Does this make any sense?

Answer 2

at the moment you have \(30\%\) of \(10\) or \(3\) gallons of anti freeze
if you add say \(x\) gallons that will add an additional \(.7x\) gallons of anti freeze
you will also have \(10+x\) gallons of mixture, which you want to be \(45\%\) anti freeze so you can set
\[3+.7x=.45(x+10)\] and solve for \(x\)

Answer 3

probably be easier to get rid of the annoying decimals by multiplying both sides by 100 and start with
\[300+70x=45(x+10)\]

Answer 4

why is it always anti freeze? who drinks that?

how much 70 proof liquor should be added to ten gallons of 30 proof punch to make it 45 proof?

that i can understand

Answer 5

Why not percentages of chocolate syrup in milk to keep it a tad more kid-friendly?

Answer 6

That is so true why antifreeze

Answer 7

But yes I get it Thanks for all your help