Question

cars produce carbon dioxide pollution. the rate they produce the pollution is measured in \\(\frac{g}{km}\\) (grams per kilometer). suppose that a family’s two cars produce a combined rate of 60 \\(\frac{g}{km}\\) of carbon dioxide pollution. during one day last week, the first car drove 35 kilometers and the second drove 25 kilometers. the two cars produced a combined total of 1700 grams of carbon dioxide pollution. at what rate does each car produce carbon dioxide pollution? first car: \\(\square \frac{g}{km}\\) second car: \\(\square \frac{g}{km}\\)

Explanation:

Step1: Define variables

Let the rate of the first car be \( x \) grams per kilometer and the rate of the second car be \( y \) grams per kilometer. We know two things: the combined rate is 60 grams per kilometer, so \( x + y = 60 \), and the total pollution from driving 35 km and 25 km respectively is 1700 grams, so \( 35x + 25y = 1700 \).

Step2: Solve the system of equations

From the first equation, we can express \( y = 60 - x \). Substitute this into the second equation:
\[

$$\begin{align*} 35x + 25(60 - x) &= 1700 \\ 35x + 1500 - 25x &= 1700 \\ 10x + 1500 &= 1700 \\ 10x &= 1700 - 1500 \\ 10x &= 200 \\ x &= 20 \end{align*}$$

\]

Step3: Find the rate of the second car

Now that we have \( x = 20 \), substitute back into \( y = 60 - x \):
\( y = 60 - 20 = 40 \)

Answer:

First car: \( 20 \frac{\text{g}}{\text{km}} \)
Second car: \( 40 \frac{\text{g}}{\text{km}} \)