Question

Question #3 3) The digits of a 2-digit number differ by 5. If the digits are interchanged and the resulting number is added to the original number, we get 99. Find the original number.

Answer 1

ones number = x

Tens number = y

y>x

Number at the tens place y = (x+5)

original number = 10 (x+5)+x

Interchange digits:= 10x+(x+5)

original number + new number = 99

¨[10(x+5)+x]+ [10x+ (x+5)] =99

Solving for x:

(10x+50+x )+( 10x+x+5) = 99

Combine like terms

(11x+50) + (11x+5) = 99

11x+11x+50+5 =99

22x+55 =99

subtract 55 from both sides

22x +55-55= 99-55

22x = 44

Divide both sides by 22

22x/22= 44/22

x = 2

unit place: 2

tens place = x+5 = 2+5 = 7

original number = 72