Question

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?

Answer 1

[AI-generated answer — Bot GPT 3.5]

a) Let's assume that the number of cars sold by Dealership A is "x" and the number of trucks sold by Dealership A is "y". Since Dealership A sells a total of 164 cars and trucks, we can write the equation as: x + y = 164.

b) Let's assume that the number of cars sold by Dealership B is "p" and the number of trucks sold by Dealership B is "q". Since Dealership B sells twice as many cars as Dealership A and half as many trucks as Dealership A, we can write the equation as: p + q = 229.

c) From equation a), we know that x + y = 164. Since we want to find the number of cars sold by Dealership A, we can set y = 0 (assuming that no trucks were sold by Dealership A). So the equation becomes: x + 0 = 164. Simplifying, we get x = 164. Dealership A sold 164 cars.

d) It is given that Dealership B sold half as many trucks as Dealership A. Since Dealership A sold y trucks, Dealership B sold (1/2)y trucks. But we don't know the value of y, so we can't calculate the number of trucks sold by Dealership B.

Answer 2

[AI-generated answer — Step-by-Step Bot]

a) Let's represent the number of cars sold by Dealership A as "x" and the number of trucks sold as "y". Since Dealership A sells a total of 164 cars and trucks, we can write the equation:

x + y = 164

b) Let's represent the number of cars sold by Dealership B as "c" and the number of trucks sold as "t". We know that Dealership B sells twice as many cars as Dealership A and half as many trucks as Dealership A. Therefore, we can write the equation:
c + t = 229
c = 2x
t = 0.5y

c) To find how many cars Dealership A sold, we can substitute the value of "y" from equation a) into equation b):
c = 2x
Substituting 164 - x (from equation a) for "y", we have:
c = 2x
164 - x = 2x
Now solve for x:
164 = 3x
x = 54.67 (approx.)

Since we cannot have a fraction of a car, we round down to the nearest whole number. Therefore, Dealership A sold 54 cars.

d) To find how many trucks Dealership B sold, we substitute the values for "x" and "y" from equation a):
t = 0.5y
t = 0.5 * 54
t = 27

Dealership B sold 27 trucks.

Answer 3

[AI-generated answer — Explain Bot]

Let's break down the information given and solve each part step by step.

a) An equation for the total cars and trucks for Dealership A:
Let's assume that the number of cars sold by Dealership A is represented by "c" and the number of trucks sold is represented by "t". We are given that Dealership A sold a total of 164 cars and trucks. Therefore, the equation can be written as:

c + t = 164

b) An equation for the total cars and trucks for Dealership B:
We are given that Dealership B sells twice as many cars as Dealership A and half as many trucks as Dealership A. Let's use the same variables "c" for cars and "t" for trucks for Dealership B as well. Now, the equation can be written as:

2c + 0.5t = 229

Note that since Dealership B sells half as many trucks as Dealership A, we multiplied the number of trucks, "t", by 0.5.

c) How many cars did Dealership A sell?
To find out the number of cars sold by Dealership A, we need to solve the equation from part a) where c + t = 164. However, we don't have enough information to determine the exact values of "c" and "t" separately. We can only find the total number of cars and trucks sold by Dealership A, which is 164.

d) Considering that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
We can again use the equation from part b) where 2c + 0.5t = 229, and substitute the total number of trucks sold by Dealership A in place of "t". Since Dealership A sold 164 cars and trucks, the number of trucks, "t", would be 164 - the number of cars, "c". Substituting this value, we can solve for "t":

2c + 0.5(164 - c) = 229
2c + 82 - 0.5c = 229
1.5c = 147
c ≈ 98

Therefore, Dealership A sold approximately 98 cars.

To find the number of trucks sold by Dealership B, we substitute the value of "c" (98) into the equation for Dealership B:

2(98) + 0.5t = 229
196 + 0.5t = 229
0.5t = 33
t ≈ 66

Therefore, Dealership B sold approximately 66 trucks.