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Nataly_w [17]
3 years ago
14

How much of a 14% iodine solution should be added to 89 ounces of a 47% iodine solution to get a 29% solution

Mathematics
1 answer:
Elza [17]3 years ago
6 0
Whatever% of anything is just (whatever/100) * anything.

x = ounces of 14% iodine.

y = ounces of 29% iodine.

we know that in a 14% iodine solution, 14% is iodine and the rest is something else, we also know that "x" ounces of the solution have 14% of iodine, how much is that?  (14/100) * x, or 0.14x.

likewise, in the 89 ounces of 47% solution there is (47/100) * 89 of iodine.

and likewise as well, in "y" ounces of 29% iodine there is (29/100) * y, or 0.29y of iodine.

bearing in mind that, whatever "x" and "y" may be, x + 89 = y, and that the sum of the iodine amounts also will equate 0.29y.

\bf \begin{array}{lccclll}
&\stackrel{ounces}{amount}&\stackrel{\%~of~iodine}{quantity}&\stackrel{iodine~oz}{amount}\\
&------&------&------\\
\textit{14\% solution}&x&0.14&0.14x\\
\textit{47\% solution}&89&0.47&41.83\\
------&------&------&------\\
mixture&y&0.29&0.29y
\end{array}
\\\\\\
\begin{cases}
x+89=\boxed{y}\\
0.14x+41.83=0.29y\\
--------------\\
0.14x+41.83=0.29\left( \boxed{x+89} \right)
\end{cases}
\\\\\\
0.14x+41.83=0.29x+25.81\implies 16.02=0.15x
\\\\\\
\cfrac{16.02}{0.15}=x\implies 106.8=x
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