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) 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?
Let's represent the number of cars sold by Dealership A as "Ca" and the number of trucks as "Ta".
We know that Ca + Ta = 164.
Let's represent the number of cars sold by Dealership B as "Cb" and the number of trucks as "Tb".
We know that Cb + Tb = 229.
We also know that Cb = 2(Ca) and Tb = 0.5(Ta).
Substituting Cb = 2(Ca) into Cb + Tb = 229, we get 2(Ca) + Tb = 229.
Substituting Tb = 0.5(Ta) into 2(Ca) + Tb = 229, we get 2(Ca) + 0.5(Ta) = 229.
Multiplying through by 2 to remove the decimal, we get 4(Ca) + Ta = 458.
Substituting Ca + Ta = 164 into 4(Ca) + Ta = 458, we get 4(Ca) + 164 = 458.
Subtracting 164 from both sides, we get 4(Ca) = 458 - 164 = 294.
Dividing both sides by 4, we get Ca = 294/4 = 73.
Therefore, Dealership A sold 73 cars.
Since Tb = 0.5(Ta), and Ta = 164 - Ca = 164 - 73 = 91, we can substitute into the equation Tb = 0.5(Ta).
Therefore, Tb = 0.5(91) = 45.
Therefore, Dealership B sold 45 trucks.
Let's solve the problem step by step:
Step 1:
Let's represent the number of cars sold by Dealership A as "x".
So, the number of trucks sold by Dealership A would be 164 - x.
Step 2:
Dealership B sells twice as many cars as Dealership A, so the number of cars sold by Dealership B would be 2x.
Dealership B sells half as many trucks as Dealership A, so the number of trucks sold by Dealership B would be (164 - x) / 2.
Step 3:
The total number of cars and trucks sold by Dealership B is given as 229. So, we can write the equation:
2x + (164 - x) / 2 = 229
Step 4:
Let's solve the equation for x:
2x + 164/2 - x/2 = 229
Multiplying through by 2 to clear the fraction:
4x + 164 - x = 458
Combining like terms:
3x + 164 = 458
Subtracting 164 from both sides:
3x = 458 - 164
3x = 294
Dividing both sides by 3:
x = 294 / 3
x = 98
Step 5:
So, Dealership A sold 98 cars.
Step 6:
To find out how many trucks Dealership B sold, we can substitute the value of x into the equation we derived earlier:
Number of trucks sold by Dealership B = (164 - x) / 2
= (164 - 98) / 2
= 66 / 2
= 33
Step 7:
Therefore, Dealership B sold 33 trucks.
To summarize:
a) Dealership A sold 98 cars.
d) Dealership B sold 33 trucks.
To find the number of cars Dealership A sold, we need to use the information given about Dealership B.
Dealership B sold twice as many cars as Dealership A, which means the number of cars Dealership A sold is half of what Dealership B sold.
So, we can find the number of cars Dealership A sold by dividing the total number of cars and trucks that Dealership B sold by 2.
Given that Dealership B sold a total of 229 cars and trucks, we divide it by 2:
229 / 2 = 114.5
Since the number of cars can not be a decimal, we can conclude that Dealership A sold 114 cars.
To find the number of trucks Dealership B sold, we will first calculate how many trucks Dealership A sold.
Since the total number of cars and trucks that Dealership A sold is 164, and we already know that Dealership A sold 114 cars,
we can subtract the number of cars from the total to find the number of trucks sold.
Trucks sold by Dealership A = Total - Cars sold by Dealership A
Trucks sold by Dealership A = 164 - 114 = 50
Since Dealership B sold half as many trucks as Dealership A, we can find the number of trucks Dealership B sold by dividing the number of trucks Dealership A sold by 2.
Trucks sold by Dealership B = Trucks sold by Dealership A / 2
Trucks sold by Dealership B = 50 / 2 = 25
Therefore, Dealership B sold 25 trucks.