Question

Madison buys mobile games via an app store on her phone. The relationship between the number of games downloaded, x, and the total cost in dollars of the downloads, y, is represented by the graph below.

What is the ratio of total cost (in dollars) to the number of games downloaded?

Answer 1

The ratio of total cost to the number of games downloaded is 6, representing a consistent increase of $6 in total cost for each additional game downloaded.

To determine the ratio of total cost to the number of games downloaded, we can use the slope of the straight line on the graph. The slope represents the rate of change, indicating how much the total cost (y) changes for each additional game downloaded (x).

Given the coordinate (9, 54) on the line, we can use the origin (0, 0) as the starting point. The slope (m) is calculated as the change in y divided by the change in x:

`\[ m = \frac{\text{change in } y}{\text{change in } x} = (54 - 0)/(9 - 0) = (54)/(9) = 6 \]`

This means that for each additional game downloaded, the total cost increases by $6.

Now, the ratio of total cost to the number of games downloaded is expressed as:

`\[ \text{Ratio} = \frac{\text{Total Cost}}{\text{Number of Games Downloaded}} = (6x)/(x) = 6 \]`

The ratio is 6, indicating that the total cost is 6 times the number of games downloaded.