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.

Question

(4 points)
a) An equation for the total cars and trucks for Dealership A:
x + y = 164

b) An equation for the total cars and trucks for Dealership B:
1/2x + 1/2y = 229
Correct?

Answer 1

Let's examine the equations for Dealership A and Dealership B more closely:

a) For Dealership A: Let \( x \) be the number of cars and \( y \) be the number of trucks. The total number of cars and trucks sold at Dealership A is given as 164. Thus, the equation is indeed: \[ x + y = 164 \]

b) For Dealership B: You noted that Dealership B sells twice as many cars and half as many trucks as Dealership A. This means:

• The number of cars sold at Dealership B is \( 2x \).
• The number of trucks sold at Dealership B is \( \frac{1}{2}y \).

The total number of cars and trucks sold at Dealership B is given as 229. Therefore, the correct equation for Dealership B should be: \[ 2x + \frac{1}{2}y = 229 \]

So, the correct equations are:

• For Dealership A: \( x + y = 164 \)
• For Dealership B: \( 2x + \frac{1}{2}y = 229 \)

Your equation for Dealership B was incorrect. It should have been \( 2x + \frac{1}{2}y = 229 \) instead of \( \frac{1}{2}x + \frac{1}{2}y = 229 \).

Answer 2

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?