# 009 Beers per Hour Algebra Question

## 2018/02/17

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### 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}]

#### Solution

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.

### More Beer Math

Check out this next beer video!