a company owns two dealerships, both of which sell cars and trucks. dealership A sells a total of 225 cars and trucks. Dealership B sells twice as many cars and half as many trucks as the dealership A, and sell a total of 300 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. given the fact that dealership B sold half as many trucks as dealership A, how many trucks did dealership B sell?
Let's assign variables to the unknown values:
Let x be the number of cars sold by dealership A.
Let y be the number of trucks sold by dealership A.
a. The equation for the total cars and trucks for dealership A is:
x + y = 225
b. Let's denote the number of cars sold by dealership B as 2x (twice as many cars as A) and the number of trucks sold as y/2 (half as many trucks as A). The equation for the total cars and trucks for dealership B is:
2x + y/2 = 300
c. Substituting x = 225 - y from equation a into equation b:
2(225 - y) + y/2 = 300
450 - 2y + y/2 = 300
Multiply the entire equation by 2 to get rid of the fraction:
900 - 4y + y = 600
-3y = -300
y = -300 / -3
y = 100
Dealership A sold 100 trucks.
d. Dealership B sold half as many trucks as dealership A, which is half of 100:
100 / 2 = 50
Dealership B sold 50 trucks.