How do you solve for this:how many gallons of a 10% alcohol solution be mixed with 20 gallons of a 10% acid solution to obtain an 8% acid solution.
Not 100% sure, but I think 5 gallons.
20 gallons of 10% acid meaning 2 gallons of acid + 18 gallon of solvent (H2O/OH).
To get it down to 8% acid, you need to dilute it to 25 gallons because you know you have 2 gallons of acid, and 2/25 - 8%. So to get 25 gallons as your final volume, you would add 5 more gallons of the 10% OH.
Note that it doesn't really matter if it's 10% OH or 100% OH... and I'm assuming that the OH has no effect to the concentration of the acid (if it's base, then it would have an effect).
how many gallons of a 10% alcohol solution be mixed with 20 gallons of a 10% acid solution to obtain an 8% acid solution?
This is college algebra not chemistry
The answer is 40/3 I just need to know how to solve it.
Strictly speaking, more information is needed for a truly correct solution due to molecular intermix between alcohol and water. In practical terms Terry is correct and his numbers are right and we will ignore the VERRY small error resulting. For the structured ALGEBRAIC solution see below
We have 20-gal of 10% acid and are going to dilute it with x-gal of 10% alcohol (presumably 0% acid) to yield (20+x)-gal of 8% acid.
--> 20(0.10)+x(0.00)=(20+x)(0.08)
--> 20(0.10)+0=20(0.08)+x(0.08)
--> 20(0.10-0.08)=x(0.08)
--> 20(0.02)=x(0.08)
X50 X50
--> 20=4x
/4 /4
--> 5=x --> x=5
I don't know where Krystal got 40/3 from but it does not work for the problem AS STATED.
Perhaps the original problem called for 5% acid instead of 10% alcohol
We have 20-gal of 10% acid and are going to dilute it with x-gal of 5% acid to yield (20+x)-gal of 8% acid.
--> 20(0.10)+x(0.05)=(20+x)(0.08)
--> 20(0.10)+x(0.05)=20(0.08)+x(0.08)
--> 20(0.10-0.08)=x(0.08-.05)
--> 20(0.02)=x(0.03)
X100 X100
--> 40=3x
/3 /3
--> 40/3=x --> x=40/3
To solve this problem, you need to use a combination of algebraic equations and the concept of concentration.
Let's break down the given information:
1) You have a 10% alcohol solution.
2) You have a 10% acid solution.
3) You want to obtain an 8% acid solution.
4) You have 20 gallons of the 10% acid solution.
Now, let's assign variables to the unknowns:
Let "x" represent the number of gallons of the 10% alcohol solution you need to mix with the 20 gallons of the 10% acid solution.
To find the amount of acid in the 10% alcohol solution, you multiply the concentration by the total volume. In this case, the concentration is 10% (0.10) and the total volume is "x" gallons.
To find the amount of acid in the 20 gallons of 10% acid solution, you multiply the concentration by the total volume. In this case, the concentration is again 10% (0.10) and the total volume is 20 gallons.
To find the amount of acid in the final 8% acid solution, you multiply the concentration by the total volume. In this case, the concentration is 8% (0.08) and the total volume will be the sum of the two solutions (x + 20) gallons.
Now, let's set up the equation:
0.10x + 0.10(20) = 0.08(x + 20)
Simplifying the equation:
0.10x + 2 = 0.08x + 1.6
0.10x - 0.08x = 1.6 - 2
0.02x = -0.4
Dividing both sides by 0.02:
x = -0.4 / 0.02
x = -20
Based on the equation, it seems like the solution is not possible. However, you should always check your solution to make sure it makes sense in the context of the problem.
In this case, a negative value for "x" is not meaningful since we cannot have a negative volume of the 10% alcohol solution. Therefore, there might have been an error or inconsistency in the information provided.
To obtain a valid solution, please double-check the given information and make sure the volumes and concentrations are correct.