The Iron-It-Out laundromat dry cleans Lila's suits.

Question

There is a proportional relationship between the number of suits Lila dry cleans, x, and the total cost (in dollars), y.
x (suits) y (dollars)
1 $8
6 $48
7 $56
9 $72
What is the constant of proportionality? Write your answer as a whole number or decimal.

Answer 1

To find the constant of proportionality \( k \) in the relationship between the number of suits \( x \) and the total cost \( y \), we can use the formula:

\[ y = kx \]

We can use any of the provided pairs of \( (x, y) \) to find \( k \).

Let's use the first pair \( (1, 8) \):

\[ 8 = k \cdot 1 \implies k = 8 \]

Now, let's verify this with the other pairs:

• For \( x = 6 \): \[ y = 8 \cdot 6 = 48 \quad \text{(which matches)} \]

• For \( x = 7 \): \[ y = 8 \cdot 7 = 56 \quad \text{(which matches)} \]

• For \( x = 9 \): \[ y = 8 \cdot 9 = 72 \quad \text{(which matches)} \]

All pairs confirm that the constant of proportionality \( k \) is indeed:

\[ \boxed{8} \]