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PSYCHO15rus [73]
3 years ago
12

The sum of digits in a two digit number formed by two digits from 1 to 9 is 8. If 9 is added to a number then both the digits be

come equal. find the number.​
Mathematics
1 answer:
Arturiano [62]3 years ago
3 0
<h2>Explanation:</h2><h2></h2>

Here we need to set a system of two linear equations in two variables. So:

  • <em>The sum of digits in a two digit number formed by two digits from 1 to 9 is 8:</em>

Let x \ and \ y be those digits, then:

x+y=8 \ \ldots eq1

  • <em>If 9 is added to a number then both the digits become equal. find the number:</em>

<em />

<em />10x+y+9 \ldots expression \ 1<em />

<em />

But from eq 1:

y=8-x

Substituting y into the expression 1:

10x+(8-x)+9=9x+17

The x-value will be found by hit and trial, so:

  • Let x = 1:

9x + 17 = 9(1)+17 = 26

We have to reject this solution because digits are different.

  • Let x = 2:

9x + 17 = 9(2)+17 = 35

We have to reject this solution because digits are different.

  • Let x = 3:

9x + 17 = 9(3)+17 = 44

<em>Then this is a two digit number formed by two equal digits. </em>

Finally, the number is:

44

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