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One-tenth of the cars in a car park are yellow. Another car arrives and now one-ninth of the cars are yellow. How many cars are now in the car park?

One-tenth of the cars in a car park are yellow. Another car arrives and now one-ninth of the cars are yellow. How many cars are now in the car park?
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1 Answer

Hi Jasun, let x represent the number of cars originally in the car park. Since 1/10 x is yellow, x must be divisible by 10. Examples 10, 20, ... 1000.
 
When 1 is added to x, x + 1, the number must be divisible by 9. Example, 80 + 1 = 81, and 81 is divisible by 9.
 
One answer is x + 1  = 81.
 
But that is not the only answer.
 
All multiples of 80 + n * 90, where n = 0, 1, 2, ...., are multiples which will satisfy the conditions of the question.
 
Example, n = 3, 80 + 270 = 350.
 
350 is divisible by 10.
 
Add 1 to 350 gives 351, which is divisible by 9.  351 / 9 = 39.
 
Therefore, 351 satisfies the question's requirements also.
 
Questions?

Comments

Perhaps I am reading your solution incorrectly, yet if the starting total is 80 the number of yellows would be 8, 8/80 = 1/10.
If the total increases by one, the fraction is 8/81 ≠ 1/9.
I have dithered with this algebraically, and got inconsistencies.
y/t = 1/10  ⇒ 10y = t
y/(t+1) = 1/9 ⇒ 9y = t + 1
Solving the system for t, 0 = t + 10!
 
Mark M (not of Bayport)