Question

The sum of the digits of a two-digit number
is 7. When the digits are interchanged, the
reversed number is 5 times the ten's digit
of the original number. Find the original
number.​

Answer 1

Answer:

Step-by-step explanation:

The sum of the digits of a two-digit number is 7.

With the digits reversed the number is 5 times the tens digit of the original number.

Find the original number.

:

Let x = the 10's digit

Let y = the units

then

10x + y = the original number

:

"The sum of the digits of a two-digit number is 7."

x + y = 7

x = (7-y); use this form for substitution

:

"With the digits reversed the number is 5 times the tens digit of the original"

10y + x = 5x

 

10y = 5x - x

10y = 4x

Substitute (7-y) for x

10y = 4(7-y)

10y = 28 - 4y

10y + 4y = 28

14y = 28

y = 28/14

y = 2

then

7 - 2 = 5 is x

:

52 is the original number