How many four-digit numbers ABCD have the property that ABCDis equal 26 times BCD? Note that x1x2...xn represents the n-digit number with digits x1x2...xn.

9514 1404 393

  9

Step-by-step explanation:

There are 9 such numbers:

  1040, 2080, 3120, 4160, 5200, 6240, 7280, 8320, 9360

For each ABCD, where BCD = x, we want ...

  26x = 1000A +x

  25x = 1000A

  x = 40A

The digit A ranges from 1 to 9 for a 4-digit number. That means there are 9 such numbers. For A=1, for example, x = 40·1 = 40, so the number ABCD is 1040. 26·BCD = 26·040 = 1040 as required.

9 is correct but if you are here from caribou math it is 7

Step-by-step explanation:

don't dislike what they said because it is the right formula. 25x = 1000A

you get 1040 2080 3120 4160 5200 6240 7280 8320 9360. But since caribou asks for bcd, b > 0 because its a 3 digit number. from that we can eliminate 1040 and 2080 getting 7

answer: -8.2562234e+13