There is a three-digit number. The second digit is four times as big as the third digit, while the first digit is three less than the second digit. What is the number?
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There is a three-digit number. The second digit is four times as big as the third digit, while the first digit is three less than the second digit. What is the number?
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QUESTION :- There is a three-digit number. The second digit is four times as big as the third digit, while the first digit is three less than the second digit. What is the number?
ANSWER :-
Since the number is a 3 digit number, number will be of the form [tex]100 \times x + 10 \times y + z[/tex].
Second digit is 4 times the third digit, [tex]y = 4 \times z[/tex]
First digit is 3 less than the second digit, [tex]x = y - 3 [/tex]
Therefore, [tex] x = 4×z - 3[/tex]
Since [tex]x[/tex] is a digit, it must lie between 1 and 9.
[NOTE :- [tex]x[/tex] cannot be 0 because if [tex]x = 0 [/tex], then it is a two digit number.]
So, [tex]z[/tex] can take values 1 and 2.
[NOTE :- [tex]z[/tex] cannot be 3 because if [tex]z = 3[/tex], then [tex]y[/tex] will not be between 1 and 9.]
So, if [tex] z = 1, x = 1[/tex] and [tex]y = 4[/tex]. Therefore, the number is 141.
If [tex] z = 2, x = 5[/tex] and [tex]y = 8[/tex]. Therefore, the number is 582.
Therefore, the possible numbers are 141 and 582.
Answer:
Since the number is a 3 digit number, number will be of the form .
Second digit is 4 times the third digit,
First digit is 3 less than the second digit,
Therefore,
Since is a digit, it must lie between 1 and 9.
[NOTE :- cannot be 0 because if , then it is a two digit number.]
So, can take values 1 and 2.
[NOTE :- cannot be 3 because if , then will not be between 1 and 9.]
So, if and . Therefore, the number is 141.
If and . Therefore, the number is 582.
Therefore, the possible numbers are 141 and 582.
Step-by-step explanation:
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