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

### 13 Answers

- charlatanLv 74 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

- Φ² = Φ+1Lv 74 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.

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- Jeff AaronLv 74 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 HLv 74 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

- llafferLv 74 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.

- L. E. GantLv 74 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....

- 4 weeks ago
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