a baker in 70 mins iced 40 cupcakes and in 49 minutes iced 28 cupcakes what is the constant of proportionality

To find the **constant of proportionality** in this context, you can set up the problem using the relationship between time and the number of cupcakes iced. The constant of proportionality (\(k\)) represents the number of cupcakes iced per minute.

We have two scenarios:

1. In 70 minutes, the baker iced 40 cupcakes.
2. In 49 minutes, the baker iced 28 cupcakes.

Since the number of cupcakes iced is directly proportional to the time, we can use the formula:

\[
\text{Constant of proportionality } (k) = \frac{\text{Number of cupcakes}}{\text{Time (in minutes)}}
\]

Now, compute \(k\) for both cases:

1. For 70 minutes and 40 cupcakes:

\[
k = \frac{40}{70} = \frac{4}{7} \quad \text{(cupcakes per minute)}
\]

2. For 49 minutes and 28 cupcakes:

\[
k = \frac{28}{49} = \frac{4}{7} \quad \text{(cupcakes per minute)}
\]

Thus, the constant of proportionality is \(\frac{4}{7}\) cupcakes per minute.

### Do you need more details or have any questions?

Here are 5 related questions:
1. How many cupcakes can the baker ice in 35 minutes?
2. If the baker worked for 100 minutes, how many cupcakes would be iced?
3. How long would it take the baker to ice 60 cupcakes?
4. What would be the constant of proportionality if the baker doubled their speed?
5. How many cupcakes could be iced in 2 hours at the same rate?

**Tip:** The constant of proportionality helps maintain a consistent rate when quantities change proportionally.

A baker in 70 mins iced 40 cupcakes and in 49 minutes iced 28 cupcakes. What is the constant of proportionality?

Learn how to calculate the constant of proportionality in a cupcake icing scenario. A baker iced 40 cupcakes in 70 minutes and 28 cupcakes in 49 minutes. Use direct variation to find the rate of cupcakes iced per minute. Suitable for students in Grades 6-8.

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