Question

1. 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 constant of proportionality

For a proportional relationship \( y = kx \), the constant of proportionality \( k \) is given by \( k=\frac{y}{x} \).

Step2: Calculate \( k \) using the first pair of values

Using \( x = 8 \) and \( y = 2.00 \), we have \( k=\frac{2.00}{8}=0.25 \).

Step3: Verify with another pair of values

Using \( x = 12 \) and \( y = 3.00 \), \( k=\frac{3.00}{12}=0.25 \).
Using \( x = 20 \) and \( y = 5.00 \), \( k=\frac{5.00}{20}=0.25 \).
All pairs give the same \( k \), so the constant of proportionality is \( 0.25 \).

Answer:

B. 0.25