I Have No Idea How To Answer This Problem?

Question

A large solar heating panel requires 110 gallons of a fluid that is 40% antifreeze. The fluid comes in either a 90% or a 25% solution. How many gallons of each should be used to prepare the 110-gallon solution?

How did you get the answer....

Answer 1

It is a Weighted Average problem. Set up an equation and solve it. Since you need 110 gallons of 40% antifreeze, the left side of the equation will be 110(.40), because the value of the antifreeze is only 40%. The right hand side will consist of the two available solutions (25% and 90%). Let x be the number of gallons of either the 25% or 90% solution. Since you need 110 gallons of solution, the other one will be 110-x. So, the right side looks like this x(.25) + (110-x)(.90) or (110-x)(.25) + x(.90). Now solve for x.
110(.4) = (110-x)(.25) + (x)(.90)
44=27.5 - .25x + .9x (remember Dist. Prop.)
16.5=.65x
x=25.4gallons of 90% solution
110-25.4 = 84.6 of 25% solution

Hope this helps!

Answer 2

To get the 40% per gallon ratio. You have 25% in one gallon, so you need 15% more soultion to equal the 40%. So, for every one 25% gallon you use, you need to add 1/6th of a 90% gallon sollution for the equasion:
25x+1/6y=110
1/6y=110-25x

x=85 (Gallons of the 25% solution)

So, I need 85 gallons of the 25% solution. knowing that for every gallon, I need to add 1/6 of the 90% solution to equal 40% per gallon:

110 - 85 = 25 (Gallons of the 90% solution)

Answer 3

Divide 90 percent by 40 percent and then add the 25 percent, that should give you a good answer.