009 Beers per Hour Algebra Question




The Beer Problem

I stayed home and pre-gamed it with 4 beers before Ubering to the bar. I can normally throw down 3 Beers each hour at the bar. I was at the bar for 4 hours. How many Beers did I consume?

The ‘b’ Value

The standard equation for a line is, (y = mx + b). As we have learned, the (b) part of the equation is where the line crosses the vertical access, often referred to as the initial condition.

Initial Condition

The b value is considered the initial condition for this problem (pre-game Beers). (Starting at the origin x = 0, or in this case, t = 0).

Let’s take a look at the figure below and break it down.

The Beer Problem

We know the initial condition, (b) is (4 Beers), giving in the problem. The rate at which beer is consumed is (\frac{3 Beers}{Hour}), which was also giving. Finally, the question asks, how many total beers after (4 hours) were consumed.

As you can see from the figure, every time an hour passes, 3 beers are consumed (count them). This corresponds with the rate or m value. Therefore, [Rate = m = \frac{3 Beers}{Hour}]


Filling in the full equation we get:

[#Beers = \frac{3 Beers}{Hour} * 4 Hours + 4 Beers = 16 Beers]

This short video describes the whole process.


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