A company owns two dealerships, both of which sell cars and trucks. Dealership A sells a total of 164 cars and trucks. Dealership B sells twice as many cars and half as many trucks as Dealership A, and sells a total of 229 cars and trucks. (4 points) a) An equation for the total cars and trucks for Dealership A: b) An equation for the total cars and trucks for Dealership B: c) How many cars did Dealership A sell? d) Considering that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?

1 answer

a) Let x be the number of cars sold by Dealership A and y be the number of trucks sold by Dealership A. The equation for the total cars and trucks for Dealership A is:

x + y = 164

b) Let a be the number of cars sold by Dealership B and b be the number of trucks sold by Dealership B. The equation for the total cars and trucks for Dealership B is:

a + b = 229

c) Since Dealership A sold a total of 164 cars and trucks, we can substitute this value into the equation from part a:

x + y = 164

x + y = 164
x + y = 164
x = 164 - y

d) Considering that Dealership B sold half as many trucks as Dealership A, we can substitute this value into the equation from part b:

a + b = 229

a + (0.5)(164 - y) = 229
a + 82 - (0.5)y = 229
a - (0.5)y = 147