# Pop vs. Water sales

## The Situation

The Brampton city council is collecting different types of data to see if people are choosing a healthier lifestyle. One of the data collected is their choice in drink over the course of one year. To collect this data they are taking information about the pop ans water sales from every store in Brampton. Are the people going a step closer to a healthier lifestyle by choosing a healthier drink?

## Variables

X (independent)- Month

Y (dependent) - Bottles sold (thousands)

## Water

Find slope with two points given (1,300) and (2,350)
• y2-y1 / x2-x1 = slope
• 350-300 / 2-1 = slope (sub in given points)
• 50 / 1 = slope
• 50 = slope

Find the value of b using y=mx+b form

• y=mx+b
• y=50x+b
• 300= 50 (1) + b (sub in one point to find the value of b)
• 300= 50+b
• 300-50=b
• 250= b

Therefore equation is y=50x+250

*note this is in thousands

## Pop

Find Slope with two points given (1,1340) and (2,1260)

• y2-y1 / x2-x1 = slope
• 1260 - 1340 / 2-1 = slope (sub in given points)
• -80 / 1= slope
• -80 = slope

Find the value of b using y = mx+b form

• y=mx+b
• y= -80x + b
• 1340 = -80(1) + b (sub in one point to find the value of b)
• 1340= -80 +b
• 1340 + 80 = b
• 1420 = b

Therefore the equation is y= -80x +1420

*note this is in thousands

## Intersection Point

Method 1:Graphing it.

Using the graph above we can conclude that the lines intersect. On the graph you can see that the lines intersect on the point (9,700). Meaning that in the 9th month (September) that store sold an equal number of pop and water, 700.

Method 2: Substituting

Equations:

-80x+ 1420 = 50x+ 250

-80x - 50x = 250 - 1420

-130x = -1,170

x = -1,170 / -130

x= 9

Now use one equation to find the value of y.

y= mx + b

y= 50(9) + 250

y= 450 +250

y= 700

Therefore you know that the points intersect at (9, 700).

## Conclusion

Going back to the question in the beginning:

Are people choosing a healthier drink?

Yes people are choosing the healthier drink (water) over the sugar filled drink (pop). Looking at the graph you can tell that over the year the number of water bottles sold is increasing while the number of pop bottles sold is decreasing, making water the more wanted choice.

## Significance of the solution

It is significant to find the solution of this linear system because it shows that over the year people are choosing a healthier drink. You can see that water sales are increasing while pop sales are decreasing. Using this linear system you can extrapolate to predict what will happen in the future.