Question

The digits of a two-digit number sum to 8. When the digits are reversed, the resulting number is 18 less than the original number. What is the original number?

Answer 1

53 add the 2 and you get 8

Step-by-step explanation:flip them 35 + 18 =53

Answer 2

53

Explanation:

Let x = the first digit

and y = the second digit. Then,

xy = the number

We have two conditions:

(1) x + y = 8

(2) 10y + x = 10x + y - 18

Simplify (2) 10y + x - 10x - y = -18

(3) 9y - 9x = -18

Multiply Equation (1) by 9 (4) 9x + 9y = 72

Add Equations (3) and (4) 18y = 54

Divide each side by 18 (5) y = 3

Substitute (5) into (1) x + 3 = 8

Subtract 3 from each side x = 5

x = 5 and y = 3

The number is 53.

Check:

(1) 5 + 3 = 8 (2) 10×3 + 5 = 10×5 + 3 - 18

8 = 8 30 + 5 = 50 + 3 - 18

35 = 53 - 18

35 = 35