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?

1 answer

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.