Question 1156383
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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.<br>
A typical algebraic solution would look something like this....<br>
x = ounces of 72% acid
85-x = ounces of 25% acid<br>
The combined acid in the two ingredients is equal to the acid in 40% of the total 85 ounces:<br>
{{{.72(x)+.25(85-x) = .40(85)}}}
{{{.72x+21.25-.25x = 34}}}
{{{.47x = 12.75}}}
{{{x = 12.75/.47 = 1275/47}}}<br>
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.<br>
Convert those numbers to decimals or percents if required....<br>
Here is a much faster path to the same ugly answers.<br>
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.<br>