Question

Thomas and zack had some toy cars. they were then given an equal number of toy cars and zack now had twice the number of toy cars as what he had at first. 2/3 of zack's toy cars were now 1/2 of thomas's toy cars. if zack had 36 more cards than thomas now, how toy cars were given to them altogether? how many toy cars dis thomas have at first?

Answer 1

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.