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.
An equation for the total cars and trucks for Dealership A:
An equation for the total cars and trucks for Dealership B:
How many cars did Dealership A sell?:
Considering that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?:
Let x be the number of cars sold by Dealership A.
Let y be the number of trucks sold by Dealership A.
We know that x + y = 164. This is the equation for the total cars and trucks for Dealership A.
Dealership B sells twice as many cars as Dealership A, so it sells 2x cars.
Dealership B sells half as many trucks as Dealership A, so it sells y/2 trucks.
The total number of cars and trucks sold by Dealership B is 229, so the equation for Dealership B is 2x + y/2 = 229.
To find the number of cars sold by Dealership A, we can solve the equation x + y = 164 for x.
Subtracting y from both sides, we get x = 164 - y.
Substituting this into the equation for Dealership B, we get 2(164 - y) + y/2 = 229.
Expanding, we get 328 - 2y + y/2 = 229.
Combining like terms, we get 328 - 229 = 2y + y/2.
99 = 2y + y/2.
Multiplying both sides by 2, we get 198 = 4y + y.
Combining like terms, we get 198 = 5y.
Dividing both sides by 5, we get y = 198/5 = 39.6.
Since Dealership B sells whole cars and trucks, we know that 39.6 trucks were sold by Dealership A.
We can round this to the nearest whole number, so Dealership A sold 40 trucks.
Therefore, Dealership A sold 164 - 40 = 124 cars.
Dealership A sold 124 cars and 40 trucks.
Let's solve this step by step:
1. To find the equation for the total cars and trucks sold by Dealership A, we can use the given information that Dealership A sells a total of 164 cars and trucks. So the equation is:
Cars + Trucks = 164 .....(Equation 1)
2. To find the equation for the total cars and trucks sold by Dealership B, we can use the given information that Dealership B sells twice as many cars and half as many trucks as Dealership A, and sells a total of 229 cars and trucks. So the equation is:
2(Cars) + (1/2)(Trucks) = 229 .....(Equation 2)
3. To find the number of cars Dealership A sold, we can substitute the values from Equation 1 into Equation 2 and solve for Cars.
Plugging in Equation 1 into Equation 2:
2(Cars) + (1/2)(Trucks) = 229
2(Cars) + (1/2)(164 - Cars) = 229 .....(Substituted Trucks with 164 - Cars from Equation 1)
Expanding:
2(Cars) + (82 - (1/2)(Cars)) = 229
2(Cars) + 82 - (1/2)(Cars) = 229
Multiply through by 2 to get rid of the fractions:
4(Cars) + 164 - Cars = 458
3(Cars) + 164 = 458
3(Cars) = 458 - 164
3(Cars) = 294
Cars = 294 / 3
Cars = 98
Therefore, Dealership A sold 98 cars.
4. Considering that Dealership B sold half as many trucks as Dealership A, we can substitute the value of Cars (98) from the previous step into Equation 1 and solve for Trucks.
Plugging in Cars = 98 into Equation 1:
Cars + Trucks = 164
98 + Trucks = 164
Trucks = 164 - 98
Trucks = 66
Therefore, Dealership B sold 66 trucks.
To summarize:
- The equation for the total cars and trucks for Dealership A is: Cars + Trucks = 164.
- The equation for the total cars and trucks for Dealership B is: 2(Cars) + (1/2)(Trucks) = 229.
- Dealership A sold 98 cars.
- Dealership B sold 66 trucks.
To solve this question, let's first define some variables:
Let's use the variable "CA" to represent the number of cars sold by Dealership A and "TA" to represent the number of trucks sold by Dealership A.
Similarly, let's use "CB" to represent the number of cars sold by Dealership B and "TB" to represent the number of trucks sold by Dealership B.
Now, let's create the equations:
1. Equation for the total cars and trucks for Dealership A:
CA + TA = 164
2. Equation for the total cars and trucks for Dealership B:
CB + TB = 229
Since the question states that Dealership B sells twice as many cars and half as many trucks as Dealership A, we can relate the variables as follows:
CB = 2 * CA (twice as many cars)
TB = (1/2) * TA (half as many trucks)
Now, let's substitute these relationships into the equations from above:
CB + TB = 229
2 * CA + (1/2) * TA = 229
CA + TA = 164
CA + (1/2) * TA = 164
Now, we have a system of equations that we can solve to find the values of CA and TA.
Solving the system of equations:
From equation 2:
2 * CA + (1/2) * TA = 229
Multiplying both sides by 2 to get rid of the fraction:
4 * CA + TA = 458
From equation 1:
CA + TA = 164
Now, we can subtract equation 1 from equation 2:
(4 * CA + TA) - (CA + TA) = 458 - 164
3 * CA = 294
Dividing both sides by 3:
CA = 98
Now that we know CA, we can substitute it back into equation 1 to find TA:
CA + TA = 164
98 + TA = 164
Subtracting 98 from both sides:
TA = 164 - 98
TA = 66
Therefore, Dealership A sold 98 cars and 66 trucks.
To answer the second question, let's use the relationship given: Dealership B sold half as many trucks as Dealership A.
Since Dealership A sold 66 trucks, Dealership B would have sold half of that:
TB = (1/2) * TA
TB = (1/2) * 66
TB = 33
Therefore, Dealership B sold 33 trucks.