A company owns two dealerships, both of which sell cars and trucks. The first dealership sells a total of 164 cars and trucks. The second dealership sells twice as many cars and half as many trucks as the first dealership, and sells a total of 229 cars and trucks
Let's say that the first dealership sold x cars and y trucks.
We know that the total sold was 164, so we can write:
x + y = 164
For the second dealership, we are told that they sell twice as many cars as the first dealership, and half as many trucks. So, the second dealership sold 2x cars and 0.5y trucks.
We know that the total sold was 229, so we can write:
2x + 0.5y = 229
Now we have two equations with two unknowns, so we can solve for x and y. We can start by multiplying the first equation by 0.5 to get:
0.5x + 0.5y = 82
Now we can subtract this equation from the second equation to eliminate y:
2x + 0.5y = 229
- 0.5x - 0.5y = -82
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1.5x = 147
Dividing both sides by 1.5 gives us x = 98. So the first dealership sold 98 cars.
We can now substitute this value of x into the first equation to find y:
98 + y = 164
y = 66
So the first dealership sold 98 cars and 66 trucks. We were told that the second dealership sold twice as many cars as the first dealership, so they sold 2 * 98 = 196 cars. We were also told that they sold half as many trucks, so they sold 0.5 * 66 = 33 trucks.
So the second dealership sold 196 cars and 33 trucks.
A company owns two dealerships, both of which sell cars and trucks. The first dealership sells a total of 164 cars and trucks. The second dealership sells twice as many cars and half as many trucks as the first dealership, and sells a total of 229 cars and trucks
Let us label the number of cars sold at the first dealership as "x" and the number of trucks sold at the same location as "y". We can set up two equations to represent the given information:
x + y = 164 (Equation 1)
The second dealership sells twice as many cars as the first dealership and half as many trucks. This can be represented as:
2x + 0.5y = 229 (Equation 2)
To solve for x and y, we can use substitution or elimination. Let's use elimination. We can multiply Equation 1 by -0.5 to get:
-0.5x - 0.5y = -82 (Equation 3)
Now we can add Equations 2 and 3 to eliminate y:
2x + 0.5y = 229
-0.5x - 0.5y = -82
---------------------
1.5x = 147
Dividing both sides by 1.5 gives us x = 98.
We can substitute this value of x into Equation 1 to solve for y:
98 + y = 164
y = 66
Therefore, the first dealership sold 98 cars and 66 trucks.
The second dealership sold twice as many cars as the first dealership, or 2*98=196 cars. The second dealership sold half as many trucks as the first dealership, or 0.5*66=33 trucks.
Therefore, the second dealership sold 196 cars and 33 trucks.
Let's break down the problem step-by-step.
Step 1: Determine the number of cars and trucks sold by the first dealership.
Let's assume the number of cars sold by the first dealership is C, and the number of trucks sold is T.
According to the problem, the first dealership sells a total of 164 cars and trucks, so we can write the equation:
C + T = 164 (Equation 1)
Step 2: Determine the number of cars and trucks sold by the second dealership.
According to the problem, the second dealership sells twice as many cars as the first dealership and half as many trucks. Let's denote the number of cars sold by the second dealership as 2C (twice the number of cars sold by the first dealership) and the number of trucks sold as T/2 (half the number of trucks sold by the first dealership).
Therefore, the second dealership sells a total of 229 cars and trucks, so we can write the equation:
2C + T/2 = 229 (Equation 2)
Step 3: Solve the system of equations (Equations 1 and 2) to find the values of C and T.
We can solve this system of equations using any method, such as substitution or elimination. Let's use the elimination method.
Multiply Equation 1 by 2 to eliminate T:
2C + 2T = 328 (Equation 3)
Multiply Equation 2 by 2 to eliminate T/2:
4C + T = 458 (Equation 4)
Subtract Equation 3 from Equation 4 to eliminate T:
4C + T - (2C + 2T) = 458 - 328
2C - T = 130 (Equation 5)
Now we have a new equation with only C and T.
Step 4: Solve Equation 5 to find the values of C and T.
Let's solve Equation 5 by adding T to both sides of the equation:
2C = T + 130
Now let's substitute the value of T + 130 in place of 2C in Equation 1:
T + 130 + T = 164
2T + 130 = 164
Subtract 130 from both sides of the equation:
2T = 164 - 130
2T = 34
Divide both sides of the equation by 2 to solve for T:
T = 34/2
T = 17
Now substitute the value of T = 17 into Equation 1 to find the value of C:
C + 17 = 164
C = 164 - 17
C = 147
Step 5: Analyze the results.
The first dealership sold 147 cars and 17 trucks.
The second dealership sold 294 cars (2 * 147) and 8.5 trucks (17/2 or 0.5 * 17).
Please note that since we cannot sell half a truck, we will assume that the second dealership sold either 8 or 9 trucks.