A car dealer received a shipment of c new cars from the car

ardz24 wrote:A car dealer received a shipment of c new cars from the car company at a base price of p dollars per car. If the dealer was able to sell d cars at a profit for f dollars each, but had to sell the rest of the cars at a loss for m dollars each, which of the following represents the total profit generated on the sales of the automobiles?

A. df – cp – mp
B. df + f(d – m) – cp
C. d(f – m) + c(m – p)
D. cp – df – f(c – d)
E. df – m(c – d) – cm

I'm confused how to set up the formulas here. Can any experts assist?

Profit from the sale of d cars = $d(f –p)
Loss from the sale of the remaining cars (= c –d) cars = $(p – m)(c –d)

The total profit generated on the sales of the automobiles = Total Profit – Total Loss = $[d(f –p) – (p – m)(c –d)].

We see that there is no option as d(f –p) – (p – m)(c –d). Let's manipulate this and see which option would match.

$d(f –p) – (p – m)(c –d) = $[df – dp –pc + pd + mc – md] = $[df –pc + mc – md] = $[d(f –m) + c (m – p)]

The correct answer: C

Hope this helps!

-Jay
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