plz solve this question as soon as possible please guys so that I can complete my holiday homework
Answers
QUESTION:
Given that,
A two digit number is 9 more than 4 times the sum of its digits if 18 is added to the number the digits interchanges their places. Find the number.
ANSWER:
Original number = 57
Step by step explanations:
given that,
A two digit number is 9 more than 4 times the sum of its digits
let the digits be x and y
so,
number be 10y + x
According to the question
10y + x = 4(x + y) + 9
10y + x = 4x + 4y + 9
10y - 4y + x - 4x = 9
6y - 3x = 9
3(2y - x) = 9
2y - x = 3....(1)
also,
given that,
if 18 is added to the number the digits interchanges their places
so,
interchanged digit number = 10x + y
original number = 10y + x
so,
10y + x + 18 = 10x + y
10y - y + x - 10x = -18
9y - 9x = -18
9(y - x) = -18
y - x = -18/9
y - x = -2. ....(2)
we have,
2y - x = 3 ...(1)
y - x = -2. (2)
(1) - (2)
2y - x - (y - x) = 3 - (-2)
2y - x - y + x = 5
y = 5
now,
putting the value of y on (1)
2y - x = 3
2(5) - x = 3
10 - x = 3
-x = 3 - 10
-x = -7
x = 7
we have,
x = 7
y = 5
original number = 10y + x
putting the values,
10(5) + 7
50 + 7
= 57
so,
Original number = 57
