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

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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) About Me  (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(39621) About Me  (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:
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Thomas and zack had some toy cars.they were given an equal number of toy cars,...
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t, Thomas
z, Zack
t=z

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..., 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?
z%2Bx=2%2Az


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2/3 of zacks toy cars were now 1/2 of Thomass toy cars.
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Not clear if another transfer of toy cars has happened, so assuming none further have been transfered,

%282%2F3%29%28z%2Bx%29=%281%2F2%29%28t-x%29


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If zack had 36 more toy cars than Thomas now.
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%282%2F3%29%28z%2Bx%29-%281%2F2%29%28t-z%29=36


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.