Question

The table shows the number of t-shirts bought $\left(x\right)$ and the total cost of the t-shirts $\left(y\right)$. Identify the equation that represents the relation between $x$ and $y$.

Number of t-shirts (x)	$5$	$25$	$26$
Cost (in $\$$) (y)	$15$	$75$	$78$

• A. $y=\left(\frac{1}{2}\right)x$
• B. $y=\left(\frac{1}{3}\right)x$
• C. $y=3x$
• D. $y=2x$

Answer 1

The correct option is C $y=3x$

To check whether there exists a proportional relationship, find the ratio of the total cost of the t-shirts (y) to the number of t-shirts bought (x) from the table.

Total cost of the t-shirts (in $\$)$ (y)	Number of t-shirts of bought (x)	$\frac{y}{x}$ (units rate)
$15$	$5$	$\frac{15}{5}=3$
$75$	$25$	$\frac{75}{25}=3$
$78$	$26$	$\frac{78}{26}=3$

From the table we can see that
$\frac{y}{x}=3$.
Thus, the equation is $y=3x$.