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.

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?

could you also make the variables be x, and y?

1 answer

a) The equation for the total cars and trucks sold by Dealership A can be represented as:

x + y = 164

where x represents the number of cars and y represents the number of trucks.

b) The equation for the total cars and trucks sold by Dealership B can be represented as:

2x + (y/2) = 229

where x represents the number of cars and y represents the number of trucks.

c) To find the number of cars sold by Dealership A, we can substitute the equation of Dealership A into the equation from part a). Solving for x:

x + y = 164
x = 164 - y

Substituting this into the equation from part b):

2(164 - y) + (y/2) = 229

Expanding and simplifying:

328 - 2y + (y/2) = 229
(4/2)(328 - 2y) + (y/2) = 229
656 - 4y + y = 458
5y = 198
y = 198/5
y = 39.6

As y represents the number of trucks and trucks cannot be in decimal numbers, we can conclude that Dealership A did not sell any trucks.

d) Since Dealership B sold half as many trucks as Dealership A, we can substitute y = 0 into the equation from part b) to find the number of trucks sold by Dealership B:

2x + (0/2) = 229
2x = 229
x = 229/2
x = 114.5

Similarly, as x represents the number of cars and cars cannot be in decimal numbers, we can determine that Dealership B sold 114 cars.