Question

A number has two digits. The digit at tens place is four times the digit at units place.. If 54
is subtracted from the number, the digits are reversed. Find the number.​

Answer 1

Answer:

Let the two digit number = 10x + y

:

"the ten's place is 3 times the digit in the unit place"

x = 3y

:

"if 54 is subtracted from the number the digits are reversed."

10x + y - 54 = 10y + x

10x - x = 10y - y + 54

9x = 9y + 54

simplify, divide by 9

x = y + 6

Replace x with 3y

3y = y + 6

3y - y = 6

2y = 6

y = 3

then

x = 3(3)

x = 9

:

93 is the number

:

:

Check solution in the statement:

"if 54 is subtracted from the number the digits are reversed."

93 - 54 = 39