QuestionA baker iced 40 cupcakes in 70 minutes and 28 cupcakes in 49 minutes. Find the constant of proportionality.

Studdy Solution

STEP 1

Assumptions1. The bakerices cupcakes at a constant rate. . The time taken to ice40 cupcakes is70 minutes.
3. The time taken to ice28 cupcakes is49 minutes.

STEP 2

To find the constant of proportionality, we need to divide the number of cupcakesiced by the time taken. Let's do this for the first set of data.
$Constant\, of\, proportionality = \frac{Number\, of\, cupcakes}{Time\, taken}$

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

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

STEP 7

Calculate the constant of proportionality.
$Constant\, of\, proportionality = \frac{28\, cupcakes}{49\, minutes} =0.57\, cupcakes/minute$ The constant of proportionality is the same for both sets of data, which confirms that the bakerices cupcakes at a constant rate. The constant of proportionality is0.57 cupcakes per minute.

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