Question 1011715: Please show me how to solve this problem
" how many numbers are there between 1 and 150 inclusive which are divisible by 5 and leave a remainder of 2 when you divide them by 3?"
Thanks
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website!
Question:
How many numbers are there between 1 and 150 inclusive which are divisible by 5 and leave a remainder of 2 when you divide them by 3?
Solution:
The number of multiples of 5 between 1 and 150 is floor(150/5)=30
where floor(x) is the greatest integer that does not exceed x.
However, question requires that these multiples must leave a remainder of 2 when divided by 3. The smallest number that satisfies this is 5, the next one is 5+(5*3)=20, where 5*3 is the product of the two factors 3 and 5. This continues as 5+(5*3)n where n is an integer, giving 5,20,35,.... as possible candidates.
This will allow you to find the number of candidates required by the question. Since you asked for the method to find it, I will leave it to you to complete the solution.
For more information, google "Chinese remainder theorem" for more explanations and examples.
|
|
|
