Question

The given table represents the proportional relationship between the two quantities $x$ and $y.$ Which of the following shows the correct values of $a$ and $b?$

$\begin{array}{cccccc}\text{Input}\left(x\right)& 2& 3& 5& 8& 11\\ \text{Output}\left(y\right)& 5& 7.5& 12.5& a& b\end{array}$

• A. $12,16.5$
• B. $16,22$
• C. $20,27.5$
• D. $17.5,22.5$

Answer 1

The correct option is C $20,27.5$

Detailed step-by-step solution:
The table represents a proportional relationship between $x$ (input) and $y$ (output).
For $x=2,y=5.$
So the ratio of $y$ to $x=\frac{y}{x}=\frac{5}{2}=2.5$
For $x=3,y=7.5$
So the ratio of $y$ to $x=\frac{y}{x}=\frac{12.5}{5}=2.5$
So the proportional relationship can be written as:$\frac{y}{x}=2.5$
$\Rightarrow y=2.5x$ (Using properties of equation)
$\therefore$ Next two inputs, $8$ and $11,$ will also follow the same proportional rule.
Hence, for $x=8,y=2.5\times 8=20,$
and for $x=11,y=2.5\times 11=\mathrm{27.5.}$
So the values of $a$ and $b$ will be $20$ and $27.5,$ respectively.
So, option B is the correct answer.