Question

Colin loves to play the piano but doesn't like practicing the exercises his piano teacher assigns. Colin knows the exercises will help him play better though, so he tries to motivate himself using his favorite treat—chocolate chip cookies.
There is a proportional relationship between the amount of time (in hours) that Colin practices the piano, x, and how many cookies he gives himself, y.
x (hours) y (cookies)
1 5
2 10
3 15
4 20
What is the constant of proportionality? Write your answer as a whole number or decimal.
cookies per hour

Answer 1

To find the constant of proportionality, we can look at the relationship between the hours practiced (x) and the cookies received (y).

In this case, the relationship can be expressed as:

\[
y = kx
\]

where \( k \) is the constant of proportionality.

From the given data:

- When \( x = 1 \), \( y = 5 \):
\[
5 = k \times 1 \implies k = 5
\]
- When \( x = 2 \), \( y = 10 \):
\[
10 = k \times 2 \implies k = \frac{10}{2} = 5
\]
- When \( x = 3 \), \( y = 15 \):
\[
15 = k \times 3 \implies k = \frac{15}{3} = 5
\]
- When \( x = 4 \), \( y = 20 \):
\[
20 = k \times 4 \implies k = \frac{20}{4} = 5
\]

In all cases, the constant \( k \) is consistently found to be \( 5 \).

Therefore, the constant of proportionality is:

\[
\boxed{5}
\]

This means Colin earns 5 cookies for every hour he practices the piano, which translates to 5 cookies per hour.