Question

The sum of the digits of a 2 digit number is 9.On reversing the digits, the new number.obtained is 45 more than the original number. Find the number.​

Answer 1

Answer:

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Given that

a + b = 9 and

[(a•10) + b] + 45 = (b•10) + a

Part 1: simplify 2nd equation

10a + b + 45 = 10b + a

45 = 9b - 9a

45/9 = b - a

5 = b - a

Part 2: eliminate one variable to solve for other variable

5 = b - a summed with

9 = a + b equals

14 = 2b

b = 7

Part 3: solve for second variable

If a + b = 9 and

b = 7, therefore

a = 2

Part 4: convert a and b digits to 2-digit numbers

Converting a and b to place-digits in 2-digit number:

if a = 2 and b = 7, the two numbers are

27 and 72

27 + 45 = 72

Answer 2

Step-by-step explanation:

The number obtained by reversing the digits is 10y + x. ATQ, reversed number is 45 more than original number.