Question

The sum of a digit of two digit number is 15 the number obtained by interchanging the digits exceed the given number by 9 find the number

Answer 1

Answer:

Let's call the two digits x and y. We know x + y = 15.

Sonce it is a two digit number, one of the digits is in the tens place and the other is in the ones place. So we can call the first number 10x + y.

The second number has the digits reversed, so that's 10y + x.

The second number is 9 more than the first. That means we can add 9 to the first number, 10x + y, to equal the second, 10y + x.

In other words, 10x + y + 9 = 10y + x.

Use inverse operations to rewrite this equation. I will subtract the 9 from both sides as well as the 10y and the x. I get 9x - 9y = -9.

Of course, this entire equation is divisible by 9, so I can divide out 9 from all terms to get this beautifully simple equation.

x - y = -1

Going back to what I knew originally, that the digits make a sum of 15, I can now write a system of equations:

x + y = 15

x - y = -1

Using the elimination method, I add this system together.

x + y = 15

+ x - y = -1

2x = 14

That's an easy solve to see that x = 7.

Once we know that, finding y is simple.

x + y = 15

7 + y = 15

y = 8

So the initial number was 78.

Step-by-step explanation:

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