SOLUTION: Hi Thomas and zack had some toy cars.they were 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 zacks toy cars were

Question 1104220: Hi
Thomas and zack had some toy cars.they were 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 zacks toy cars were now 1/2 of Thomass toy cars. If zack had 36 more toy cars than Thomas now.
how many toy cars were given to them altogether.
How many toy cars did Thomas have at first.
Thanks
Found 2 solutions by Theo, josgarithmetic:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
this problem has some logical inconsistencies which i believe lead to no solution being possible.

let's just look at what zack and tom have now.

you are given that 2/3 of zack's toy cars now = 1/2 of thomas' toy cars now.

if you let z = the number of zack's toys now, and you let t = the number of thomas' toys now, then you get 2/3 * z = 1/2 * t.

you are also given that the number of zack's toys now is 36 more than the number of thomas' toys now.

this leads to z = t + 36.

in the formula of 2/3 * z = 1/2 * t, you can replace z with t + 36 to get 2/3 * (t + 36) = 1/2 * t.

multiply both sides of this equation by 6 and you get 4 * (t + 36) = 3 * t

simplify to get 4 * t + 144 = 3 * t

subtract 3 * t from both sides of this equation and sibtract 144 from both sides of this equation and you get t = -144.

the number of toys that either zack or tom have can't be negative.

if this problem is supposed to have a solution, then it would be good to know what that solution is supposed to be.

i've tried it several times and have always wound up with a negative solution.

that's why i think it can't be solved the way it's being presented.

Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
This problem description is bad, or seems bad.

Here is an attempt to just begin:
---
Thomas and zack had some toy cars.they were given an equal number of toy cars,...
---

t, Thomas
z, Zack

---
..., and zack now had twice the number of toy cars as what he had at first.
---

Some amount, x cars was taken from Thomas and given to Zack?

---------
2/3 of zacks toy cars were now 1/2 of Thomass toy cars.
---------

Not clear if another transfer of toy cars has happened, so assuming none further have been transfered,

-----
If zack had 36 more toy cars than Thomas now.
-----

To summarize the system of equations, the description can mean this:

and maybe this system can be solved for t, z, and x.
-
NO! the last two equations of the system do NOT agree with each other.

Recheck your problem description, and if you want help, then give the exact problem description, word-for-word exactly as it is given to you.
RELATED QUESTIONS
Hi thomss and zack had some toy cars.they were given an equal number of toy cars and zack (answered by ankor@dixie-net.com)
Hi Tom had some toy cars 2/5 of them were red. He has 35 more green cars than red cars.... (answered by ikleyn,greenestamps,timofer)
Hello, Question: The ratio of the number of toy cars to the number of toy trains in a (answered by Boreal,solver91311)
There were some red yellow and blue toy cars in a box. 3/8 of the toy cars were red and... (answered by josgarithmetic,ikleyn)
Alex had Y toy cars. He gave 11 of them to his friend. Later his dad bought him twice as... (answered by Okamiden)
Becker has 7 blue cars,4 green cars , and 8 red cars in his toy car collection.what is... (answered by themasterofcircuits)
Alexa and Zack are solving the following problem: The number of miles on Car A is 50... (answered by ankor@dixie-net.com,Silver_surfer,greenestamps)
An auto dealership had to reduce the number of cars in its lot by 700 cars. In the... (answered by checkley77)
Peter had 30 game cards and Manuel had 75 game cards after they were given an equal... (answered by josmiceli)