A dental hygiene company is creating a new 24 -ounce tube of toothpaste by
combining its most popular toothpastes, Cavity Crusher and Bad Breath
Obliterator. Cavity Crusher contains \(0.25 \%\) of sodium fluoride as its
active ingredient, and Bad Breath Obliterator contains \(0.30 \%\) of triclosan
as its active ingredient for a total of \(0.069\) ounces of active ingredients
in both toothpastes. Solving which of the following systems of equations
yields the number of ounces of Cavity Crusher, \(c\), and the number of ounces
of Bad Breath Obliterator, \(b\), that are in the new toothpaste?
A)
$$
\begin{aligned}
c+b & =0.069 \\
0.25 c+0.3 b & =24
\end{aligned}
$$
$$
\begin{aligned}
c+b & =24 \\
0.0025 c+0.003 b & =0.069
\end{aligned}
$$
B)
C)
D)
$$
\begin{aligned}
c+b & =24 \\
0.025 c+0.03 b & =0.069 \\
c+b & =24 \\
0.25 c+0.3 b & =0.069 \\
\frac{2 d^2-d-10}{d^2+7 d+10} & =\frac{d^2-4 d+3}{d^2+2 d-15}
\end{aligned}
$$