QuestionFind the constant of proportionality for a baker who iced 40 cupcakes in 70 minutes and 28 cupcakes in 49 minutes.

Studdy Solution

STEP 1

Assumptions1. The bakericed40 cupcakes in70 minutes. . The bakericed28 cupcakes in49 minutes.
3. The rate at which the bakerices cupcakes is constant.

STEP 2

We can find the constant of proportionality by dividing the number of cupcakes by the time taken. Let's do this for the first scenario.
$Constant\, of\, proportionality = \frac{Number\, of\, cupcakes}{Time\, taken}$

STEP 3

Now, plug in the given values for the number of cupcakes and time taken in the first scenario to calculate the constant of proportionality.
$Constant\, of\, proportionality = \frac{40\, cupcakes}{70\, minutes}$

STEP 4

Calculate the constant of proportionality for the first scenario.
$Constant\, of\, proportionality = \frac{40\, cupcakes}{70\, minutes} =0.57\, cupcakes/minute$

STEP 5

Now, let's calculate the constant of proportionality for the second scenario.
$Constant\, of\, proportionality = \frac{Number\, of\, cupcakes}{Time\, taken}$

STEP 6

Now, plug in the given values for the number of cupcakes and time taken in the second scenario to calculate the constant of proportionality.
$Constant\, of\, proportionality = \frac{28\, cupcakes}{49\, minutes}$

STEP 7

Calculate the constant of proportionality for the second scenario.
$Constant\, of\, proportionality = \frac{28\, cupcakes}{49\, minutes} =0.57\, cupcakes/minute$

STEP 8

As we can see, the constant of proportionality is the same in both scenarios. Therefore, the constant of proportionality is0.57 cupcakes per minute.
The constant of proportionality is0.57 cupcakes per minute.

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