If 250 = 15a + b, a and b are both non-negative integers, and b<15, what is the value of b?

13 Answers

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  • 4 weeks ago

    15*16=240

    B=10.................................

  • 4 weeks ago

    250 = 15a + b,

    (250 - b)/15=a

    (250-b) must be a multiple/product of 15

    just less than 250.

    so a=16 and b=10

  • 4 weeks ago

    Hint: This can be thought off (more simply) as 250 ÷ 15 = a remainder b, so b = 250 mod 15 in the stated range.

  • 4 weeks ago

     15a + b = 250

     If b < 15,

     a = 16 and b = 10

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  • 4 weeks ago

    15a = 250 - b

    0 < b < 15

    0 > -b > -15

    250 > 250 - b > 250 - 15

    250 > 15a > 235

    250/15 > a > 235/15

    Approximately: 16.666 > a > 15.666

    Since a is an integer, a = 16

    250 = 15*16 + b

    250 = 240 + b

    b = 250 - 240 = 10

  • Ian H
    Lv 7
    4 weeks ago

    Need 15a to be less than but close to 250

    240 is 16*15 so a is 16

    That makes b = 250 - 240 = 10

  • sepia
    Lv 7
    4 weeks ago

    250 = 15a + b

    a = 16 and b = 10

  • 4 weeks ago

    If you are told that:

    a and b are non-negative integers where b < 15, and:

    250 = 15a + b

    Since we only have one equation we can't solve this without a little brute force.  Let's solve this for a in terms of b to see what happens:

    250 - b = 15a

    (250 - b) / 15 = a

    to have "a" be an integer, (250 - b) must be a multiple of 15.  We only have 0-14 to ch oose from, so one of these numbers must do it.  Let's see what happens if b = 0:

    (250 - 0) / 15 = 250/15 = 16 R 10

    Since the remainder is 10, we need to subtract 10 more to make it work.  Testing b = 10:

    (250 - 10) / 15 = 240/15 = 16

    So a = 16 when b = 10.

  • 4 weeks ago

    ==> a = 250/15 - b/15

    ==> a = 50/3 - b/15 = 16 + 2/3 - b/15

    since a is a whole number and b < 15,

    then b/15 must be 2/3

    so b/15 = 2/3

    ==> b = 10

    hence a must be 17 as well:

    15 * 16 + 10 = 250 as a check....

  • 250 = 15a + b

    b < 15

    Just for fun, let b = 15

    250 = 15a + 15

    250 = 15 * (a + 1)

    50 = 3 * (a + 1)

    16.666666.... = a + 1

    15.666666.... = a

    Now for fun, let b = 0

    250 = 15a + 0

    250 = 15a

    50 = 3a

    16.666666.... = a

    15.6666666... < a < 16.6666666.....

    a is an integer.  Therefore a is 16

    250 = 15 * 16 + b

    250 = 240 + b

    10 = b

    a = 16 , b = 10

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