Question

The sum of the digits of a given two digits the new numbers is 5 .if the digits are reversed, the new number is reduced by 27 . find the given number ​

Answer 1

Answer:. The numbers are 41 and 14

Step-by-step explanation: X and Y represent the digits. In the Tens place, the digit has 10× its base value. Therefore we can set up equations to model the information given:

10x+y = 10y + x +27

X + Y = 5

y =5-x rewritten to substitute for y

10x + 5-x = 10(5-x)+x +27

Distribute and then combine like terms:

9x +5 = 50 - 9x +27

Add 9x to both sides; subtract 5 from both sides.

9x +9x = 50+27-5

18x = 72 Combine like terms. Then divide both sides to solve for x.

x = 4

4+y=5 Substitute 4 for x; solve for y.

y=1

Substitute values of x and Y into the original equation and check.

40 +1 = 10 +4 + 27

41 = 14+ 27

True! 41=41

The numbers are 41 and 14.