Calculate the values of x and y in the following table. $\begin{array}{|l|l|l|l|}
\hline \text { Gear A } & &\text { Gear B } \
\hline \begin{array}{l}
\text { Number of } \
\text { teeth }
\end{array} & \text { rpm } & \begin{array}{l}
\text { Number of } \
\text { teeth }
\end{array} & \mathrm{rpm} \
\hline 10 & 100 & x & 125 \
\hline 260 & y & 50 & 520 \
\hline
\end{array}$
A) x = 8, y = 25
B) x = 2, y = 200
C) x = 8, y = 100
D) x = 16, y = 200
E) x = 16, y = 25

Question

Calculate the values of x and y in the following table.   $\begin{array}{|l|l|l|l|}
\hline \text { Gear A } & &\text { Gear B } \
\hline \begin{array}{l}
\text { Number of } \
\text { teeth }
\end{array} & \text { rpm } & \begin{array}{l}
\text { Number of } \
\text { teeth }
\end{array} & \mathrm{rpm} \
\hline 10 & 100 & x & 125 \
\hline 260 & y & 50 & 520 \
\hline
\end{array}$
A) x = 8, y = 25
B) x = 2, y = 200
C) x = 8, y = 100
D) x = 16, y = 200
E) x = 16, y = 25

Quizplus · Accepted Answer

To find the ratio of the number of teeth between gears A and B, we can set up the proportion: $\frac{10}{x} = \frac{100}{125}$. Solving for $x$, we get $x=8$. We can also set up the proportion $\frac{260}{50} = \frac{y}{520}$ and solve for $y$ to get $y=1040$. However, we need to convert the units of $y$ to rpm, which can be done by dividing by the number of teeth on Gear B: $\frac{1040}{50} = 20.8$ rpm. Since $y$ must be a whole number of rpm, we round 20.8 to 21 rpm. Therefore, the values of $x$ and $y$ are $8$ and $21$, respectively, which corresponds to choice C.

Calculate the Values of X and Y in the Following