Question

a number of cosisting of two digits is such that when multiplied by 9, it becomes equal to twice the number obtained by reversing the order of the digit in the original number. If the difference of two digits of the number is 7. Find the number.

Answer 1

Define x and y:

Let x be the digit on the ones place

Let y be the digit in the tens place

The number is (10y + x)

If the number is multiplied by 9, it is twice the number obtained by reversing the order of the number

9(10y + x) = 2(10x + y)

90y + 9x = 20x + 2y

88y = 11x

8y = x -----------------------[ 1 ]

Given that the difference of teh two digit is 7

x - y = 7 -----------------------[ 2 ]

Equations:

8y = x -----------------------[ 1 ]

x - y = 7 -----------------------[ 2 ]

Find y:

Sub [ 1 ] into [ 2 ]:

8y - y = 7

7y = 7

y = 1

Find x:

Sub y = 1 into [ 1 ]

x = 8(1)

x = 8

Find the number:

Number = 10y + x = 10(1) + 8 = 18

Answer: The number is 18