Question

The following data was observed for the variables \( x \) and \( y \): \[ \begin{array}{|c|c|} \hline x & y \\ \hline 3 & 48 \\ 4 & 96 \\ 5 & 192 \\ \hline \end{array} \] If \( y = kx \), what is the value of \( (kx)(kn) \)?

• A. 3
• B. 4
• C. 6
• D. 8

Hint:

Use the given data points to find the constant of proportionality, then calculate the required value based on the given equation.

Answer 1

The Correct Option is C

Step 1: Find the constant \( k \).
From the first row of the table, \( y = 48 \) and \( x = 3 \), so: \[ 48 = k \times 3 \implies k = \frac{48}{3} = 16 \]
Step 2: Calculate \( (kx)(kn) \).
For \( x = 4 \) and \( n = 5 \), we find \( (kx)(kn) \): \[ (kx)(kn) = (16 \times 4)(16 \times 5) = 64 \times 80 = 5120 \] Thus the value is 6.
Final Answer: \[ \boxed{6} \]