The sum of the digits of a 2-digit number is 7. If the digits are reversed, the new number increases by 3
less than 4 times the original number. Find the original number
Answers
Step-by-step explanation:
16, 61
1 + 6 = 7
61 = 4(16) - 3
Let’s set original number at (10x +y) and the reversed digit number as (10y + x).
It has already been defined that x + y = 7.
The reversed digit number will be (4 * (original number)) - 3
10y + x = 4(10x + y) -3
Solve for y.
y = -1/2 + (13/2)x
Plug into x + y = 7, and solve for x.
x = 1
Therefore, y = 6
1 + 6 = 7
10(6) + 1 = 4(10(1) +6) - 3
61 = 40 + 24 - 3
61 = 61
EXPLANATION.
Let the digit at ten's place be = x
Let the digit at unit place be = y
original number = 10x + y
reversing number = 10y + x
To find the original number.
According to the question,
Case = 1.
The sum of digit of two digit number = 7
=> x + y = 7 ........(1)
Case = 2.
If the digit are reversed,the new number
increase by 3 less than 4 times the original
number.
=> 10y + x = 4 ( 10x + y) - 3
=> 10y + x = 40x + 4y - 3
=> 6y - 39x = -3
=> 2y - 13x = -1 .......(2)
From equation (1) and (2) we get,
=> multiply equation (1) by 13
=> multiply equation (2) by 1
we get,
=> 13x + 13y = 91
=> 2y - 13x = -1
=> 15y = 90
=> y = 6
put the value of y = 6 in equation (1)
we get,
=> x + 6 = 7
=> x = 1
Therefore,
original number = 10x + y = 10(1) + 6 = 16.