The sum of the digits of a certain two-digit number is 9. When you reverse its digits you increase the number by 63. What is the

Question

3 years ago

10

number?

1 answer:

DENIUS [597] · Answer 1 · 2022-09-03T01:59:31+03:00

2-digit number is 18

Step-by-step explanation:

Let x= ten's digit and

y= one's digit

The sum of two digits is 9

so, x+y = 9

When you reverse its digits you increase the number by 63.

10y+x=10x+y+63

10y-y+x-10x=63

9y-9x=63

So, we have two equations:

$x+y = 9\,\,and\,\,9y-9x=63$

Solving these equations to find value of x and y:

Let:

$x+y = 9\,\,\,eq(1)\\9y-9x=63\,\,\,eq(2)$

Multiply eq(1) by 9 and add both equations:

$9x+9y = 81\,\,\,\\-9x+9y=63\\--------\\18y=144\\y=144/18\\y=8$

So, value of y=8

Now, finding value of x:

Putting value of y in eq(1)

$x+y=9\\x+8=9\\x=9-8\\x=1$

So, value of x=1

The value of x is 1 and value of y = 8

So, 2-digit number is 18

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