The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number? *
1 point
Answers
Step-by-step explanation:
Given :-
The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143.
To find :-
What can be the original number?
Solution :-
Let the digit at units place in the two digit number be Y
The place value of Y = 1×Y = Y
Let the digit at tens place in the two digit number be X
The place value of X = 10×X = 10X
The original number = 10X+Y
If the digits are reversed then the new number= 10Y+X
Given that :-
The digits of a two-digit number differ by 3
X-Y = 3 ----------(1)
On adding the original number and the new number then
=> 10X+Y+X+10Y
=> (10X+X)+(Y+10Y)
=> 11X+11Y
According to the given problem
The sum of the original number and the new number = 143
=> 11X+11Y = 143
=> 11(X+Y) = 143
=> X+Y = 143/11
=> X+Y = 13 ---------(2)
On adding (1)&(2)
X-Y = 3
X+Y = 13
(+)
__________
2X + 0 = 16
__________
=> 2X = 16
=> X = 16/2
=> X = 8
On Substituting the value of X in (2)
=> 8+Y = 13
=> Y = 13-8
=> Y = 5
The digit at Ones place = 5
The digit at Tens place = 8
The number = 85
Answer:-
The Original number for the given problem is 85
Check:-
The digit at Ones place = 5
The digit at Tens place = 8
The difference between the digits
= 8-5 = 3
The number = 85
The new number obtained by reversing the digits = 58
Their sum = 85+58 = 143
Verified the given relations in the given problem.
Used Method:-
- Elimination method
Answer:
The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number?
Step-by-step explanation:
Step-by-step explanation:
Given :-
The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143.
To find :-
What can be the original number?
Solution :-
Let the digit at units place in the two digit number be Y
The place value of Y = 1×Y = Y
Let the digit at tens place in the two digit number be X
The place value of X = 10×X = 10X
The original number = 10X+Y
If the digits are reversed then the new number= 10Y+X
Given that :-
The digits of a two-digit number differ by 3
X-Y = 3 ----------(1)
On adding the original number and the new number then
=> 10X+Y+X+10Y
=> (10X+X)+(Y+10Y)
=> 11X+11Y
According to the given problem
The sum of the original number and the new number = 143
=> 11X+11Y = 143
=> 11(X+Y) = 143
=> X+Y = 143/11
=> X+Y = 13 ---------(2)
On adding (1)&(2)
X-Y = 3
X+Y = 13
(+)
__________
2X + 0 = 16
__________
=> 2X = 16
=> X = 16/2
=> X = 8
On Substituting the value of X in (2)
=> 8+Y = 13
=> Y = 13-8
=> Y = 5
The digit at Ones place = 5
The digit at Tens place = 8
The number = 85
Answer:-
The Original number for the given problem is 85
Check:-
The digit at Ones place = 5
The digit at Tens place = 8
The difference between the digits
= 8-5 = 3
The number = 85
The new number obtained by reversing the digits = 58
Their sum = 85+58 = 143
Verified the given relations in the given problem.