Posted by **Krish** on Friday, December 27, 2013 at 4:10pm.

How many ordered pairs of natural numbers (n, m) are there that solve the equation

2n + 3m = 100

- Math -
**Damon**, Friday, December 27, 2013 at 5:02pm
Well we could argue about if zero counts as a natural number. If it does then

2n will always be zero or even

2 n = 0 2 4 6 8 ...... 50 ....100

3 m is zero or a multiple of 3

3 m = 0 3 6 9 12 15 ....33 .... 99

now the sum of those must be 100, which is even so delete all the odd 3ms

3 m = 0 6 12 18 24 .... 90 96

now which could add to 100

4 + 96

10 + 90

16 + 84

22 + 78

28 + 72 add six, subtract 6, see pattern

34 + 66

40 + 60

46 + 54

52 + 48

58 + 42

64 + 36

70 + 30

76 + 24

82 + 18

88 + 12

94 + 6

100 + 0 count them :)

## Answer this Question

## Related Questions

- Math - How many ordered pairs (x, y) of counting numbers (x = 1, 2, 3, · · · , ...
- MATH - A function machine accepts inputs as ordered pairs. the componets of the ...
- MATH!!! - A function machince accepts inputs as ordered pairs. The componeys of ...
- math - hese numbers in ordered pairs are related to each other. 1.(1,2), (3,4...
- Math - these numbers in ordered pairs are related to each other. 1.(1,2), (3,4...
- Math - these numbers in ordered pairs are related to each other. 1.(1,2), (3,4...
- math - A function machine accepts inputs as ordered pairs. The Components of the...
- Alg 1 - Graph -4x+y>-6 5y<=-x-20 Then give 2 ordered pairs that solve it& ...
- Algebra - Please check my answer. Solve the system of linear equalities ...
- Math/Check - I have a few problems I need you to take a look at and tell me if ...