Answer: Let's denote the number of toy cars that Thomas had at first as T, and the number of toy cars that they were given each as x.
After they were given an equal number of toy cars, Zack had twice the number of toys cars as he had at first, which means that Zack had 2x toy cars.
Also, we know that 2/3 of Zack's toy cars were now 1/2 of Thomas's toy cars, so we can write:
2/3 * 2x = 1/2 * (T + x)
Multiplying both sides by 3/2:
2x = 3/4T + 3/4x
Simplifying:
5/4x = 3/4T
Since Zack has 36 more toy cars than Thomas now, we can write:
2x - x = T + x - 36
Simplifying:
x = T/3 + 12
We can now substitute x in the second equation:
5/4(T/3 + 12) = 3/4T
Multiplying both sides by 12:
5T/4 + 60 = 9T/4
Subtracting 5T/4 from both sides:
T/2 = 60
T = 120
So Thomas had 120 toy cars at first, and they were given a total of:
2 * x + T + 2x - (T + x) = 3x + 2T = 3(T/3 + 12) + 2T = 5T + 108 = 708
Toy cars altogether.