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?

Question

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?

Answer 1

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.

 

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