Question

what is the four-digit number in which the first digit is one-third the second, the third is the sum of the first and second, and the last is three times the second?​

Answer 1

First digit:

Find the multiples of 3 which is a 1 digit number.

Multiples of 3: 3,6,9...

`(1)/(3) * 3 = 1`

`(1)/(3) * 6 = 2`

`(1)/(3) * 9 = 3`

Third digit:

`1 + 3 = 4`

`2 + 6 = 8`

`3 + 9 = 12`

(3+9=12) will be rejected because the first and second digit add up should be a 1 digit number for third digit.

Last digit:

`3 * 3 = 9`

`3 * 6 = 18`

`3 * 9 = 27`

(3×6=18) and (3×9=27) will be eliminated as the numbers are too large.

Thus, the answer is 1349.

Answer 2

1,349

Explanation:

Using the verbal descriptions from the problem, we can set up the following expressions for each number:

first: 'one-third the second' =
`(1)/(3)x`

second: 'x'

third: 'the sum of the first and second' =
`(1)/(3)x` + x =
`(4)/(3)`

fourth: 'three times the second' = 3x

Since the four-digit number has to be whole numbers, the first choice would be the integer '3':

first:
`(1)/(3)*3=1`

second: x = 3

third:
`(4)/(3)*3=4`

fourth: 3x = 3(3) = 9

final answer: 1,349