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When you arrive at the family reunion, Uncle Blake has already started eating mini hot dogs. 3 minutes later, he has eaten a total of 39 hot dogs. 5 minutes after you arrived he finished 61 of them.

What is his rate? _____ dogs per minute.

How many had he eaten when you arrived? _____ hot dogs

Write an equation to model this situation (use m for minutes and d for hot dogs).

Respuesta :

The relationship between the number of hot dogs eaten and time after

arrival is a linear relationship.

  • First question; His rate is; 11 dogs per minute
  • Second question; The number of hot dogs he has eaten was; 6 hot dogs

Reasons:

First question:

The given parameters are;

Number of hot dogs Uncle Blake has eaten after 3 minutes = 39 hot dogs

Number of hot dogs eaten after 5 minutes = 61 hot dogs

Therefore, we have that the points on a graph of hot dog eaten are;

(3, 39), and (5, 61)

Which gives;

[tex]The \ rate \ of \ hot \ dog \ eating = \dfrac{(61 - 39) \ hot \ dogs}{(5 - 3) \ minutes} = 11 \ hot \, dogs/minute[/tex]

  • His rate is 11 hot dogs/minute

Second question;

From the given rate, we have the following equation;

n - 39 = 11·(t - 3)

n = 11·t - 33 + 39

n = 11·t + 6

The above equation for the number of hot dogs eaten is in the form, a straight line equation, y = m·x + c.

Where;

y = n = The number of hot dogs eaten

x = t = The time since arrival

c = 6 = The y-intercept

At the time of arrival, t = 0, therefore;

n = 11 × 0 + 6 = 6

  • The number of hot dog he had eaten at arrival = 6 hot dogs

Learn more here:

https://brainly.com/question/19538210

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