r 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: 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?
a) Let's represent the total number of cars and trucks sold by Dealership A as "x." So, the equation for the total cars and trucks for Dealership A is:
x = 164 (since Dealership A sells a total of 164 cars and trucks)
b) Dealership B sells twice as many cars (2x) and half as many trucks (0.5x) as Dealership A. So, the equation for the total cars and trucks for Dealership B is:
2x + 0.5x = 229 (since Dealership B sells a total of 229 cars and trucks)
c) To find out how many cars Dealership A sold, we substitute the value of x from equation a) into equation b) and solve for it. So:
2(164) + 0.5(164) = 229
328 + 82 = 229
410 = 229
Therefore, Dealership A sold 164 cars.
d) Considering that Dealership B sold half as many trucks as Dealership A, we can find the number of trucks sold by Dealership B by dividing the number of trucks sold by Dealership A by 2:
Number of trucks sold by Dealership B = 0.5(164) = 82
So, Dealership B sold 82 trucks.
a) Let's assume that the number of cars sold by Dealership A is x and the number of trucks sold by Dealership A is y.
According to the given information, the total cars and trucks sold by Dealership A is 164. Therefore, we can write the equation as:
x + y = 164
b) Let's assume that the number of cars sold by Dealership B is p and the number of trucks sold by Dealership B is q.
According to the given information, Dealership B sells twice as many cars as Dealership A. Therefore, we can write the equation as:
p = 2x
Dealership B sells half as many trucks as Dealership A. Therefore, we can write the equation as:
q = 0.5y
The total cars and trucks sold by Dealership B is 229. Therefore, we can write the equation as:
p + q = 229
c) To find the number of cars sold by Dealership A, we substitute the value of y = 164 - x into the equation:
x + (164 - x) = 164
164 = 164
x = 0
Therefore, Dealership A sold 0 cars.
d) Considering that Dealership B sold half as many trucks as Dealership A, we can substitute the value of y = 164 - x into the equation:
q = 0.5(164 - x)
q = 82 - 0.5x
Substituting the values of p = 2x and q = 82 - 0.5x into the equation:
2x + (82 - 0.5x) = 229
2x - 0.5x = 229 - 82
1.5x = 147
x = 98
Therefore, Dealership B sold 98 trucks.
a) Let's assume that 'x' represents the number of cars sold at Dealership A and 'y' represents the number of trucks sold at Dealership A. The equation for the total cars and trucks sold at Dealership A can be written as:
x + y = 164
b) Given that Dealership B sells twice as many cars as Dealership A and half as many trucks as Dealership A, we can express the total cars and trucks sold at Dealership B as:
2x + (1/2)y = 229
c) To find out how many cars Dealership A sold, we need to solve the equation in part a) for 'x'. Rearranging the equation, we get:
x = 164 - y
Substituting this value of 'x' into equation b), we can solve for 'y'.
2(164 - y) + (1/2)y = 229
328 - 2y + (1/2)y = 229
Multiplying through by 2 to get rid of the fractions:
656 - 4y + y = 458
Combining like terms:
656 - 3y = 458
Rearranging the equation:
-3y = 458 - 656
-3y = -198
Dividing both sides by -3:
y = 66
So, Dealership A sold 66 trucks.
d) Given that Dealership B sold half as many trucks as Dealership A, we can multiply the number of trucks sold at Dealership A by 1/2:
Number of trucks sold at Dealership B = (1/2) * 66 = 33
Therefore, Dealership B sold 33 trucks.