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When Li Juan's auto yard is filled to capacity with only cars, it has $60$ cars. When it is filled to capacity with only vans, it has $50$ vans. Which linear equation models the number of cars, $c$ , and vans, $v$ , that could be in Li Juan's auto yard when it is filled to capacity? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{c}{60}+\frac{v}{50}=1$ $\newline$ (B) $60c+50v=1$ $\newline$ (C) $\frac{c}{50}+\frac{v}{60}=1$ $\newline$ (D) $50c+60v=1$

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Descartes' Rule of Signs

Full solution

Q. When Li Juan's auto yard is filled to capacity with only cars, it has

60

cars. When it is filled to capacity with only vans, it has

50

vans. Which linear equation models the number of cars,

c

, and vans,

v

, that could be in Li Juan's auto yard when it is filled to capacity?

\newline

Choose

1

answer:

\newline

(A)

\frac{c}{60}+\frac{v}{50}=1

\newline

(B)

60c+50v=1

\newline

(C)

\frac{c}{50}+\frac{v}{60}=1

\newline

(D)

50c+60v=1

Prompt: question_prompt: Find the linear equation that models the number of cars, $c$ , and vans, $v$ , in Li Juan's auto yard when it is at full capacity.
Maximum Cars Point: If the yard is full with $60$ cars and no vans, then the number of cars is at its maximum. This can be represented by the point $(60, 0)$ on the graph where $c$ is on the x-axis and $v$ is on the y-axis.
Maximum Vans Point: Similarly, if the yard is full with $50$ vans and no cars, then the number of vans is at its maximum. This can be represented by the point $(0, 50)$ on the graph.
Forming Linear Equation: The two points $(60, 0)$ and $(0, 50)$ can be used to form a straight line equation in the form of $(\frac{c}{x}) + (\frac{v}{y}) = 1$ , where $x$ is the maximum number of cars and $y$ is the maximum number of vans.
Final Equation: Plugging in the values for $x$ and $y$ , we get $\frac{c}{60}$ + $\frac{v}{50}$ = $1$ . This equation represents all the combinations of cars and vans that can fill the yard to capacity.

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