Question

at a school carnival, tickets can be purchased to participate in different activities. the table shows the total cost for different numbers of tickets. school carnival

number of tickets, x	total cost, y (dollars)
12	3.00
20	5.00
30	7.50
50	12.50

what is the constant of proportionality that relates y, the total cost in dollars, to x, the number of tickets purchased?
a 4.00
b 0.25
c 1.00
d 0.10

Explanation:

Step1: Recall the formula for direct - proportion

The equation for a proportional relationship is $y = mx$ (where $b = 0$ for a proportional relationship, and $m$ is the constant of proportionality). We can find $m$ using the formula $m=\frac{y}{x}$.

Step2: Choose a pair of values from the table

Let's take the pair $(x = 30,y = 7.50)$.

Step3: Calculate the constant of proportionality

$m=\frac{y}{x}=\frac{7.50}{30}=0.25$. We can check with another pair, say $(x = 50,y = 12.50)$. Then $m=\frac{y}{x}=\frac{12.50}{50}=0.25$.

Answer:

B. 0.25