Math

posted by .

How many ordered pairs of natural numbers (n, m) are there that solve the equation
2n + 3m = 100

  • Math -

    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 :)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra

    Please check my answer. Solve the system of linear equalities graphically. 3x-y<=6 x>=1 y<=3 For the answer I have: Equation in slope intercept form: Equation 1:y-intercept as ordered pair=> (0, -6) Equation 1: x-intercept …
  2. Math/Check

    I have a few problems I need you to take a look at and tell me if I arrived at the right answer. 1. I am to use the intercepts to graph the equation x+3y=6 I used the formula y=mx+b using 3 and -6 for x I got these as my ordered pairs …
  3. Alg 1

    Graph -4x+y>-6 5y<=-x-20 Then give 2 ordered pairs that solve it& 2 ordered pairs that don't solve it
  4. Math

    How many ordered pairs (x, y) of counting numbers (x = 1, 2, 3, · · · , and y = 1, 2, 3, · · ·) satisfy the equation x + 2y = 100?
  5. Math

    these numbers in ordered pairs are related to each other. 1.(1,2), (3,4), (5,6), (0,__), (10,11), (2,___), (___,7), (8,__) 2. (9,3), (3,1), (12,__), (__,2), (___,7), (8,___) 3. (4,9), (5,11), (2,5), (6,__), (__,7), (10,__), (__,3) …
  6. math

    hese numbers in ordered pairs are related to each other. 1.(1,2), (3,4), (5,6), (0,__), (10,11), (2,___), (___,7), (8,__) 2. (9,3), (3,1), (12,__), (__,2), (___,7), (8,___) 3. (4,9), (5,11), (2,5), (6,__), (__,7), (10,__), (__,3) 4. …
  7. Math

    these numbers in ordered pairs are related to each other. 1.(1,2), (3,4), (5,6), (0,__), (10,11), (2,___), (___,7), (8,__) 2. (9,3), (3,1), (12,__), (__,2), (___,7), (8,___) 3. (4,9), (5,11), (2,5), (6,__), (__,7), (10,__), (__,3) …
  8. math

    A function machine accepts inputs as ordered pairs. The Components of the order pairs are natural numbers and the first components is the length of the rectangle and the second componet is the width . The given machine computs the …
  9. MATH

    A function machine accepts inputs as ordered pairs. the componets of the ordered pairs are natural numbers and the first component is the length of rectangle and the second comonet is the width . the given machince comptes the perimiter …
  10. MATH!!!

    A function machince accepts inputs as ordered pairs. The componeys of the ordered pairs are natural numbers and the first componet is the length of the rectangle and the second componet is the width. the given machince comptes the …

More Similar Questions