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

From the first equation, x + y = 164, we can isolate x to find x = 164 - y.

Substitute this value of x in the second equation: 2x + 1/2y = 229.

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

328 - 2y + 1/2y = 229

Multiply through by 2 to remove the fraction: 656 - 4y + y = 458

Combine like terms: 656 - 3y = 458

Subtract 656 from both sides: -3y = -198

Divide both sides by -3: y = 66

Substitute this value of y back to the first equation: x + 66 = 164

Subtract 66 from both sides: x = 98

Dealership A sold 98 cars.

Dealership B sold 66 trucks.