Use your graphing calculator: Desmos Graphing Calculator%0D%0A%0D%0AA 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 sells a total of 300 cars and trucks. %0D%0A%0D%0A(4 points)%0D%0Aa) An equation for the total cars and trucks for Dealership A: %0D%0A%0D%0Ab) An equation for the total cars and trucks for Dealership B: %0D%0A%0D%0Ac) How many cars did Dealership A sell? %0D%0A%0D%0Ad) Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?

Answer 1

a) Let x be the number of cars sold by Dealership A, and let y be the number of trucks sold by Dealership A. The equation for the total cars and trucks sold by Dealership A can be written as:
x + y = 225

b) Dealership B sells twice as many cars as Dealership A, so the number of cars sold by Dealership B is 2x. Dealership B sells half as many trucks as Dealership A, so the number of trucks sold by Dealership B is (1/2)*y. The equation for the total cars and trucks sold by Dealership B can be written as:
2x + (1/2)*y = 300

c) To find out how many cars Dealership A sold, we can solve the equation x + y = 225 for x. Substituting y = 225 - x, we get:
x + (225 - x) = 225
2x = 225
x = 112.5

Dealership A sold 112.5 cars.

d) Given that Dealership B sold half as many trucks as Dealership A, the number of trucks sold by Dealership B can be found by substituting y = 225 - x into the equation for Dealership A. We get:
(1/2)*y = (1/2)*(225 - x)
y = (225 - x)/2
Substituting x = 112.5, we get:
y = (225 - 112.5)/2
y = 112.5/2
y = 56.25

Dealership B sold 56.25 trucks.