1967 AMC 12 Problem 8

Attempt Problem 8 of the 1967 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1967 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

m

ounces of an

m\%

solution of acid,

x

ounces of water are added to yield an

(m-10)\%

solution. If

m\gt25,

then

x

is:

\dfrac{10m}{m-10}

\dfrac{5m}{m-10}

\dfrac{m}{m-10}

\dfrac{5m}{m-20}

not determined by the given information

The amount of acid remains

\frac{m^2}{100}

ounces

Set that equal to

\frac{m-10}{100}

times the final volume

m+x

Conservation of acid gives

\frac{m^2}{100} =\frac{m-10}{100}(m+x).

Hence

m^2=(m-10)(m+x),

10m=(m-10)x

and

x=\frac{10m}{m-10}.

Therefore, the correct answer is A.

Problem 8 in other years