Question

6. A certain number of two digits is three times the sum of its digits. If 45 be added to it, the digits are reversed. The number is:

Answer 1

Let a = the 10's digit

let b = the units

then

10a + b = the number

:

A certain number of two digits is three times the sum of the digit.

10a + b = 3(a + b)

10a + b = 3a + 3b

10a - 3a = 3b - b

7a = 2b

If 45 is added to it the digits are reversed.Find the number.

10a + b + 45 = 10b + a

10a - a + 45 = 10b - b

9a + 45 = 9b

simplify, divide by 9

a + 5 = b

a = b - 5

Back to our 1st equation, replace a with (b-5)

7(b-5) = 2b

7b - 35 = 2b

7b - 2b = 35

5b = 35

b = 7

find a using the equation; a = b - 5

a = 7 - 5

a = 2

Our number: 27

:

:

Confirm this in the statement:

"If 45 is added to it the digits are reversed"

27 + 45 = 72

Thank You..

Mark me as Brainlist