Respuesta :
Answer: The possible digits are 2,5 and 8
Step-by-step explanation:
3x +486 = 100_
From the equation in the question, we are looking for a digit to put in the gap after 100 to make sure that when we solve the question, x will be a whole number.
Therefore, since it's a single digit required, the possible digits will be from 0 to 9.
Now, from divisibilty tests, for a number from 2 digits upwards to be divisible by 3, the sum of its digits has to be divisible by 3.
Going back to the question, let's divide each term by 3 to get ;
3x/3 + 486/3 = 100_ to give ;
x + 162 = 100_ /3
Now for x to be a whole number, the value on the right hand side must be a whole number.
Therefore, since we know that for a 2 digits and above number to be divisible by 3,it's sum must be divisible by 3. We can plug in any of the digits from 0-9 into the gap and add up.
For 0; 1+0+0+0= 1
For 1; 1+0+0+1 = 2
For 2; 1+0+0+2= 3
Following the same addition pattern for digits 3,4,5,6,7,8and 9, we'll get sum of 4,5,6,7,8,9 and 10 respectively.
Inspecting the above, the only additions that are divisible by 3 are when the digit is; 2,5 and 8
