b) Let's define x as the number of cars sold by Dealership A, and y as the number of trucks sold by Dealership A. Equations for Dealership A and Dealership B can be written as:
Dealership A: x + y = 164
Dealership B: 2x + (1/2)y = 229
c) From equation a), we know that x + y = 164. Rearranging the equation to solve for x, we get:
x = 164 - y
Substituting this expression for x into equation b), we get:
2(164 - y) + (1/2)y = 229
Simplifying the equation:
328 - 2y + (1/2)y = 229
328 - 2y + y/2 = 229
Subtracting 328 from both sides:
-2y + y/2 = -99
Multiplying both sides by 2 to get rid of the fraction:
-4y + y = -198
Simplifying the equation:
-3y = -198
Solving for y:
y = (-198)/(-3) = 66
d) Substituting the value of y into equation a), we can solve for x:
x + 66 = 164
Subtracting 66 from both sides:
x = 164 - 66 = 98
So, Dealership A sold 98 cars, and Dealership B sold 66 trucks.
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: x + y = 229 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?
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