The Unruly Queens chess club is hosting a tournament, and each club member is bringing something to eat or drink. Kristen decides to bring oatmeal raisin cookies from her favorite bakery.

Question

There is a proportional relationship between the number of oatmeal raisin cookies Kristen buys, x, and their total cost (in dollars), y.
x (cookies) y (dollars)
10 $10
11 $11
17 $17
19 $19
What is the constant of proportionality? Write your answer as a whole number or decimal.
dollars per cookie

Answer 1

To find the constant of proportionality in this scenario, we look at the relationship between the number of cookies $x$ and the total cost $y$.

The constant of proportionality can be calculated by dividing the total cost $y$ by the number of cookies $x$.

From the provided data:

$$\text{Constant of proportionality}=\frac{y}{x}$$

Calculating for the provided pairs:

1. For $x=10$, $y=10$: $$\frac{10}{10}=1$$

2. For $x=11$, $y=11$: $$\frac{11}{11}=1$$

3. For $x=17$, $y=17$: $$\frac{17}{17}=1$$

4. For $x=19$, $y=19$: $$\frac{19}{19}=1$$

In each case, we find that the constant of proportionality is $1$ dollar per cookie.

Thus, the constant of proportionality is:

$$\boxed{{\displaystyle 1}}$$