Answer:
1,349
Step-by-step explanation:
Using the verbal descriptions from the problem, we can set up the following expressions for each number:
first: 'one-third the second' = [tex]\frac{1}{3}x[/tex]
second: 'x'
third: 'the sum of the first and second' = [tex]\frac{1}{3}x[/tex] + x = [tex]\frac{4}{3}[/tex]
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: [tex]\frac{1}{3}*3=1[/tex]
second: x = 3
third: [tex]\frac{4}{3}*3=4[/tex]
fourth: 3x = 3(3) = 9
final answer: 1,349
First digit:
Find the multiples of 3 which is a 1 digit number.
Multiples of 3: 3,6,9...
[tex] \frac{1}{3} \times 3 = 1[/tex]
[tex] \frac{1}{3} \times 6 = 2[/tex]
[tex] \frac{1}{3} \times 9 = 3[/tex]
Third digit:
[tex]1 + 3 = 4[/tex]
[tex]2 + 6 = 8[/tex]
[tex]3 + 9 = 12[/tex]
(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:
[tex]3 \times 3 = 9[/tex]
[tex]3 \times 6 = 18[/tex]
[tex]3 \times 9 = 27[/tex]
(3×6=18) and (3×9=27) will be eliminated as the numbers are too large.
Thus, the answer is 1349.
