Question

The table and graph shows the relation between the number of chairs sold $“n”$ and the cost of the chairs $“c”$ in shop A and shop B, respectively. Select the correct statement.

Shop A:

Number of chairs sold (n)	$2$	$6$	$8$
Cost of the chairs (in $\$$) (c)	$24$	$72$	$96$

Shop B:

• A. Both are proportional with different equations
• B. Both are non proportional with the same equations
• C. Both are non proportional with different equations
• D. Both are proportional with the same equations

Answer 1

The correct option is D Both are proportional with the same equations

From the table,

Number of chairs sold (n)	Cost of the chairs (in $\$$) (c)	Cost per chair $=\frac{c}{n}$
$2$	$24$	$\frac{24}{2}=12$
$6$	$72$	$\frac{72}{6}=12$
$8$	$96$	$\frac{96}{8}=12$

We see that $\frac{c}{n}=12$.
Hence,
$c=12n$
From the graph, $\text{Slope},"m"=\frac{\text{Rise}}{\text{Run}}=\frac{36-24}{3-2}=\frac{12}{1}=12$
Equation of the proportional line is:
$y=mx$
$c=12n$
Hence, both the table and the graph represents a proportional relationship where they form the same equation.