Question

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.

An equation for the total cars and trucks for dealership A:
x + y = 164

An equation for the total cars and trucks for dealership B:
2x + 1/2y = 229

How many cars did dealership A sell?

How many trucks did the dealership B sell?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the number of cars sold by dealership A, we need to solve the equation:

x + y = 164

Similarly, to find the number of trucks sold by dealership B, we need to solve the equation:

2x + 1/2y = 229

To solve the first equation, we can isolate x:

x = 164 - y

Now we can substitute this expression for x in the second equation:

2(164 - y) + 1/2y = 229

Expanding and simplifying:

328 - 2y + 1/2y = 229

Combining like terms:

-2y + 1/2y = 229 - 328

Multiplying the fraction by 2 to eliminate the denominator:

-4y + y = -99

Simplifying:

-3y = -99

Dividing both sides by -3:

y = (-99)/(-3) = 33

Now we can substitute this value back into the first equation to find x:

x + 33 = 164

x = 164 - 33 = 131

So, dealership A sold 131 cars and dealership B sold 33 trucks.

Answer 2

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

To find the number of cars dealership A sold, we can use the first equation x + y = 164, where x represents the number of cars and y represents the number of trucks.

To find the number of trucks dealership B sold, we can use the second equation 2x + (1/2)y = 229.

Answer 3

[AI-generated answer — Explain Bot]

To find the number of cars sold by dealership A, we can use the equation x + y = 164, where x represents the number of cars sold and y represents the number of trucks sold.

To find the number of trucks sold by dealership B, we can use the equation 2x + (1/2)y = 229, where x represents the number of cars sold and y represents the number of trucks sold.

To solve these equations, we can use substitution or elimination method.

Let's use the elimination method:

Multiply the first equation by 2 to eliminate the x variable:
2(x + y) = 2(164)
2x + 2y = 328

Next, subtract the second equation from the multiplied first equation to eliminate the x variable:
(2x + 2y) - (2x + (1/2)y) = 328 - 229
2x + 2y - 2x - (1/2)y = 99
(2y - (1/2)y) = 99
(3/2)y = 99

Multiply both sides by 2/3 to solve for y:
(3/2)y * (2/3) = 99 * (2/3)
y = 66

Now substitute this value of y into the first equation to solve for x:
x + 66 = 164
x = 164 - 66
x = 98

Therefore, dealership A sold 98 cars and dealership B sold 66 trucks.