Let's call the number of cars sold by the first dealership C1 and the number of trucks sold T1.
Given that the first dealership sells a total of 164 cars and trucks, we can write the equation:
C1 + T1 = 164
The second dealership sells twice as many cars as the first dealership, so the number of cars sold by the second dealership is 2C1. The second dealership also sells half as many trucks as the first dealership, so the number of trucks sold by the second dealership is (1/2)T1.
Given that the second dealership sells a total of 229 cars and trucks, we can write the equation:
2C1 + (1/2)T1 = 229
To solve this system of equations, we can first eliminate the variable T1 by multiplying the first equation by 2:
2(C1 + T1) = 2(164)
2C1 + 2T1 = 328
Now we can substitute this expression for 2T1 in the second equation:
2C1 + (1/2)T1 = 229
2C1 + (1/2)(164 - C1) = 229
2C1 + 82 - (1/2)C1 = 229
(3/2)C1 + 82 = 229
(3/2)C1 = 229 - 82
(3/2)C1 = 147
3C1 = 294
C1 = 294/3
C1 = 98
Now we can substitute this value for C1 in the first equation to find T1:
98 + T1 = 164
T1 = 164 - 98
T1 = 66
Therefore, the first dealership sold 98 cars and 66 trucks, while 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.
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