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.
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) Equation for the total cars and trucks for Dealership A: A = 164
b) Equation for the total cars and trucks for Dealership B: B = 2C + T, where C represents the number of cars and T represents the number of trucks sold by Dealership B.
c) Dealership A sold 164 cars.
d) Since Dealership B sold half as many trucks as Dealership A, we can substitute T in equation b) with T = (1/2)T from equation a), which gives B = 2C + (1/2)T. We know that B = 229 from the problem statement, so 229 = 2C + (1/2)T. Solving the equation for T, we get T = 78. Therefore, Dealership B sold 78 trucks.
a) Let's represent the number of cars sold by Dealership A as "C" and the number of trucks sold as "T". According to the information given, Dealership A sells a total of 164 cars and trucks. Therefore, the equation for the total cars and trucks for Dealership A is:
C + T = 164
b) Let's represent the number of cars sold by Dealership B as "C" and the number of trucks sold as "T". According to the information given, Dealership B sells twice as many cars and half as many trucks as Dealership A, and sells a total of 229 cars and trucks. Therefore, the equation for the total cars and trucks for Dealership B is:
2C + (1/2)T = 229
c) From equation (a) C + T = 164, we can deduce that C = 164 - T. Since there is no additional information given to calculate the exact value of C, we cannot determine the number of cars Dealership A sold.
d) Considering that Dealership B sold half as many trucks as Dealership A, we know that T = (1/2)T_A. Substituting this into equation (b), we get:
2C + (1/2)T_A = 229
2C + (1/2)(2T) = 229
2C + 1T = 229
Since we have no additional information to solve for C or T, we cannot determine the number of trucks Dealership B sold.
a) Let's denote the number of cars sold at Dealership A as "C_a" and the number of trucks sold as "T_a". We are given that Dealership A sells a total of 164 cars and trucks. Therefore, we can write the equation:
C_a + T_a = 164
b) Now, let's denote the number of cars sold at Dealership B as "C_b" and the number of trucks sold as "T_b". We are given that Dealership B sells twice as many cars as Dealership A and half as many trucks. Therefore, we can write the equation:
C_b = 2C_a
T_b = 0.5T_a
The total number of cars and trucks sold at Dealership B is given as 229, so we can write the equation:
C_b + T_b = 229
c) We need to find the number of cars sold at Dealership A, which is denoted as "C_a". We can substitute the equation C_b = 2C_a into the equation C_a + T_a = 164:
2C_a + T_a = 229
T_a = 229 - 2C_a
Now, we can substitute T_a back into the first equation:
C_a + (229 - 2C_a) = 164
229 - C_a = 164
C_a = 229 - 164
C_a = 65
Therefore, Dealership A sold 65 cars.
d) Now, we need to find the number of trucks sold at Dealership B, which is denoted as "T_b". We know that T_b = 0.5T_a. Since we have already found the value of T_a as 229 - 2C_a, we can substitute it into the equation:
T_b = 0.5(229 - 2C_a)
T_b = 0.5(229 - 2*65)
T_b = 0.5(229 - 130)
T_b = 0.5(99)
T_b = 49.5 (rounded to the nearest whole number)
Therefore, Dealership B sold 49 trucks.