Question

For a particular model of moving truck, rental agency A charges a daily fee of m dollars, plus n cents per mile. For the same model of truck, rental agency B charges a daily fee of p dollars, plus q cents per mile. If a driver plans to rent this model of truck for two days, which of the following expressions gives the number of miles this driver must drive for the two rental agencies’ total charges to be equal?(A) 100(m−p)q−n100(m−p)q−n(B) 200(p−m)n−q200(p−m)n−q(C) 50(m−p)q−n50(m−p)q−n(D) 2(p−m)n−q2(p−m)n−q(E) m−p2(q−n)

Answer 1

Answer: 2(p-m)/(n-q) D

Step-by-step explanation: Let x be the number of days of rental and y the miles the driver is going to drive.

A equation for Rental Agency A: mx + ny

A equation for Rental Agency B: px + qy

For 2 days, x = 2

A: m2 + ny = 2m + ny

B: p2 + qy = 2p + qy

And we want a function of y when A = B

A = B

2m + ny = 2p + qy

ny - qy = 2p - 2m

y(n - q) = 2(p - m)

y = 2(p - m)/(n - q)