SOLUTION: Misty wishes to obtain 85 ounces of a 40% acid solution by combining a 72% acid solution with a 25% acid solution. How much of each solution should misty use?

Question 1156383: Misty wishes to obtain 85 ounces of a 40% acid solution by combining a 72% acid solution with a 25% acid solution. How much of each solution should misty use?
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

Let x = the number of ounces of the stronger (72%) Let y = the number of ounces of the weaker (25%) We make this chart and fill in what is given: Acid-H20 solution | Oz. of liquid | % Pure | Oz. of Pure acid | --------------------------------------------------------------- Stronger Strength | x | 72% | | Weaker Strength | y | 25% | | ------------------|-------------------------------------------- Medium Strength | 85 | 40% | | Then we take the percentages to get the number of ounces of PURE acid in each solution, of the stronger and weaker before mixing, and of the medium strength after mixing. Acid-H20 solution | Oz. of liquid | % Pure | Oz. of Pure acid | --------------------------------------------------------------- Stronger Strength | x | 72% | 0.72x | Weaker Strength | y | 25% | 0.25y | ------------------|-------------------------------------------- Medium Strength | 85 | 40% | 0.40(85) | Our two equations come from the first and last columns: Solve the system by substitution or elimination. As a visual partial check, since the percentage of the final mixture (40%) is nearer to the percentage of the weaker solution (25%) than it is to the stronger solution, we expect that the answer should be so that it takes more of the weaker solution than of the stronger solution. Edwin

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

You should understand how to solve a two-part mixture problem like this using formal algebra. But if a formal algebraic solution is not required, there is a MUCH faster way to solve the problem.

A typical algebraic solution would look something like this....

x = ounces of 72% acid
85-x = ounces of 25% acid

The combined acid in the two ingredients is equal to the acid in 40% of the total 85 ounces:

The amount of 72% acid is 1275/47 ounces; the amount of 25% acid is 85-(1275/47) = 2720/47 ounces. Those are ugly fractions; and we had to do a lot of ugly calculations to find them.

Convert those numbers to decimals or percents if required....

Here is a much faster path to the same ugly answers.

On a number line, 40% is 15/47 of the way from 25% to 72%.
That means 15/47 of the mixture needs to be the 72% acid.
15/47 of the total 85 ounces is 1275/47 ounces.

RELATED QUESTIONS
Misty wishes to obtain 85 oz of a 40% solution by combining a 72% acid solution with a... (answered by jorel1380)
How many ounces of a 25% acid solution should be mixed with a 50% acid solution to... (answered by Fombitz)
A 1.5% acid solution is mixed with a 4% acid solution. How many ounces of each solution... (answered by Fombitz)
How many liters of a 15% acid solution should be mixed with 30 liters of a 40% acid... (answered by lostin)
A 5% acid solution is mixed with a 9% acid solution. How many ounces of the 5% acid... (answered by stanbon)
How many ounces of a 35% acid solution should be mixed with a 60% acid solution to get 40 (answered by mananth,ikleyn)
Acid solution A is composed of 12.5% hydrochloric acid and acid solution B is composed of (answered by stanbon)
If Julie is mixing a 5% acid solution with a 9% acid solution, how many ounces of each... (answered by Alan3354)
A chemist has three different acid solutions. The first acid solution contains 25% acid,... (answered by greenestamps,Theo,josgarithmetic)