Let's say dealership A sold X cars and Y trucks.
From the information given, we can create two equations.
The first equation states that dealership A sells a total of 164 cars and trucks: X + Y = 164.
The second equation states that dealership B sells twice as many cars and half as many trucks as dealership A, and sells a total of 229 cars and trucks.
Since dealership B sells half as many trucks as dealership A, the equation for the trucks will be Y/2.
So the second equation is: 2(X) + (Y/2) = 229.
Now we can solve this system of equations.
Multiply the first equation by 2 to eliminate Y:
2X + 2Y = 328.
Multiply the second equation by 2 to eliminate the denominator:
4X + Y = 458.
Now, subtract the first equation from the second equation:
(4X + Y) - (2X + 2Y) = 458 - 328.
2X - Y = 130.
Now, add this equation to the first equation:
(2X - Y) + (X + Y) = 130 + 164.
3X = 294.
Finally, divide both sides of the equation by 3 to solve for X:
X = 294 / 3.
X = 98.
Therefore, dealership A sold 98 cars.
To find the number of trucks dealership B sold, plug X = 98 into the second equation:
2(98) + (Y/2) = 229.
196 + (Y/2) = 229.
Y/2 = 229 - 196.
Y/2 = 33.
Multiply both sides of the equation by 2 to find Y:
Y = 2 * 33.
Y = 66.
Therefore, dealership B sold 66 trucks.
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.
How many cars did Dealership A sell?
Considering that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
1 answer