The sum of the digits of a three-digit number is 12. The tens digit is 2 less than the hundreds digit, and the units digit is 4 less than the sum of the other two digits. What is the number?
Answers
Answered by
29
Step-by-step explanation:
the number should be 534
Attachments:
Answered by
77
Answer:-
Let the digit at hundred's place be x , digit at ten's place y and digit at one's place be z.
⟶ The number = 100x + 10y + z.
Given:
Sum of the digits = 12
⟶ x + y + z = 12 -- equation (1)
Ten's digit is 2 less than the hundreds digit.
⟶ y = x - 2 -- equation (2)
Also,
unit's digit is 4 less than sum of the other two digits.
⟶ z = (x + y) - 4
Substitute the value of y from equation (2).
⟶ z = x + x - 2 - 4
⟶ z = 2x - 6 -- equation (3)
Substitute the values of y & z in equation (1).
⟶ x + x - 2 + 2x - 6 = 12
⟶ 4x - 8 = 12
⟶ 4x = 12 + 8
⟶ 4x = 20
⟶ x = 20/4
⟶ x = 5
Substitute the value of x in equation (2).
⟶ y = 5 - 2
⟶ y = 3
Substitute the value of x in equation (3)
⟶ z = 2(5) - 6
⟶ z = 10 - 6
⟶ z = 4
Hence,
The number = 100(5) + 10(3) + 4 = 300 + 10 + 8 = 534.
Therefore, the required 3 - digit number is 534.
Similar questions