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? Choose 1 answer: (A) (c)/( 60)+(v)/( 50)=1 (B) 60 c+50 v=1 (C) (c)/( 50)+(v)/( 60)=1 (D) 50 c+60 v=1

Question

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? Choose 1 answer: (A)  (c)/( 60)+(v)/( 50)=1 (B)  60 c+50 v=1 (C)  (c)/( 50)+(v)/( 60)=1 (D)  50 c+60 v=1

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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 (c/x) + (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 (c/60) + (v/50) = 1. This equation represents all the combinations of cars and vans that can fill the yard to capacity.

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