Saturday

September 20, 2014

September 20, 2014

Posted by **Jacob** on Sunday, November 4, 2007 at 5:45pm.

- Math -
**Jacob**, Sunday, November 4, 2007 at 6:12pmi ment what is a number that divied by 3 has a remainder of 2 also that same number divided by 4 has a remainder 3 and that same number divided by 5 has a remainder of 4

- Math -
**drwls**, Sunday, November 4, 2007 at 6:20pmIt must be 2 more than a number evenly divisible by 3, such as

5,8,11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59 ...

It must also be 3 more than a number evenly divisible by 4, such as

7,11,15,19,23,27,31,35,39, 43,47, 51, 55, 59...

It must also be 4 more than a number evenly divisble by 5, such as

9,15,19,24, 29, 34, 39, 44, 49, 54, 59, 64, 69..

The smallest number that satisfies all requirements is 59. There will probably be larger numbers also.

- Math -
**tchrwill**, Sunday, November 4, 2007 at 6:25pmwhat is a number that divied by 3 has a remainder of 2 also that smae number divided by 4 has a remainder 3 and that same number divided by 5 has a remainder of 4

Here is another version of the famous Chinese Remainder puzzles which should give you an idea as to how to go about solving it. There are other methods.

Lets now attack the problem where three divisors and remainders are involved.

What is the smallest number that will leave a remainder of 1 when divided by 5, a remainder of 2 when divided by 7, and a remainder of 3 when divided by 9?

Let

1--N/5 = A + 1/5 or N = 5A + 1

2--N/7 = B + 2/7 or N = 7B + 2

3--N/9 = C + 3/9 or N = 9C + 3

4--Combining (1) and (2), 5A + 1 = 7B + 2 or 5A - 7B = 1 or B = (5A - 1)/7.

4--Derive the first values of A and B by trial and error. Subsequent values of A differ by the coefficient of B or 7 and subsequent values of B differ by the coefficient of A, 5.

5--A.....3.....10.....17.....24.....31.....38.....45

....B.....2......7.....12.....17.....22.....27.....32

6--Combining (2) and (3), 7B + 2 = 9C + 3 or 7B - 9C = 1 or C = (7B - 1)/9.

7--Derive the first values of B and C by trial and error. Subsequent values of B differ by the coefficient of C or 9 and subsequent values of C differ by the coefficient of B, or 7.

8--B.....4.....13.....22.....31.....40.....49.....58

....C....3......10.....17.....24.....31.....38.....45

9--Combining (3) and (1), 9C + 3 = 5A + 1 or 5A - 9C = 2 or A = (9C + 2)/5

10--Derive the first values of C and A by trial and error. Subsequent values of C differ by the coefficient of A or 5 and subsequent values of A differ by the coefficient of C, or 9.

11--C.....2.....7.....12.....17.....22.....27.....32

.....A.....4....13....22......31....40.....49......58

12--We must now search the tabular data to find a consistent set of values acrossall three tables.

13--The lowest consistent set is A = 31, B = 22 and C = 17.

14--This then leads to the minimum N = 5(31) + 1 = 7(22) + 2 = 9(17) + 3 = 156.

- Math -
**Macey Davis**, Friday, October 10, 2008 at 7:58pmhbjbjgingginkgofgmogf

**Answer this Question**

**Related Questions**

math - my daughter needs help finding a mystery number. 1)when the mystery ...

math - What is the lowest numberthat has a remainder of 1 when divided by 2 and ...

math - what is the least common positive integer that meets the following ...

math - what is the least common positive integer that meets the following ...

math - A certain number has a remainder of 3 when divided by 5. That same number...

Math - How many integers between 200 and 500 inclusive leave a remainder 1 when ...

Math - How many integers bewteen 200 and 500 inclusive leave a remainder 1 when ...

number theory - Find the least positive integer that leaves the remainder 3 ...

Math - This problem from China is almost 2000 years old: Find a number that when...

math - This problem from China is almost 2000 years old: Find a number that when...