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Difficulty: MediumInterpreting Linear Relationships in Context

A commercial printing press has a reservoir of yellow ink. The volume of yellow ink in the reservoir, VV, in milliliters, after printing pp pages of a color brochure is modeled by the equation V=1,200−0.15pV = 1,200 - 0.15p. According to the model, what is the decrease, in milliliters, in the volume of yellow ink in the reservoir for every 100 pages printed?

Answer: 15 milliliters

Answer

The volume of yellow ink in the reservoir decreases by 15 milliliters for every 100 pages printed.
In the equation V=1,200−0.15pV = 1,200 - 0.15p, the coefficient of pp is −0.15-0.15. This represents the rate of change of the volume of yellow ink in the reservoir with respect to the number of pages printed. Specifically, it means the volume decreases by 0.150.15 milliliters for each additional page printed. To find the decrease in volume for every 100 pages printed, multiply the rate per page by 100: 0.15×100=150.15 \times 100 = 15 milliliters.

Step-by-Step Solution

1
Identify the rate of change per page from the linear equation.
The rate of change is 0.15 milliliters per page.
In the linear equation V=1,200−0.15pV = 1,200 - 0.15p, the coefficient of the independent variable pp represents the change in the dependent variable VV for each unit increase in pp.
2
Calculate the decrease in ink volume for 100 pages.
15 milliliters
Since the volume decreases by 0.15 milliliters for each page printed, printing 100 pages results in a total decrease of 0.15×100=150.15 \times 100 = 15 milliliters.

Key Concept

Interpreting the slope (rate of change) of a linear equation in context.
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Topics

Interpreting Linear Relationships in Context

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