Question

the
sum
Two digit number
4 more
times
its digits.
of
is
substracted
number
from
digits
reversed I ind numbers
If 18
the​

Answer 1

Answer:

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Step-by-step explanation:

MATHS

A two digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number, the digits are reversed. Find the number.

ANSWER

Let x= ones digit and y=tens digit

According to the question ,

∴x+10y=6(x+y)+4

⇒10y=6x+6y+4−x

⇒4y=5x+4

And , from if 18 is substracted from the number , the digits are reversed ,

∴x+10y−18=y+10x

⇒10y−18=y+9x

⇒9y−18=9x

⇒y−2=x

Substitute x value into :

4y=5x+4

4y=5(y−2)+4

4y=5y−6

y=6

Substitute y into :

∴y−2=x

⇒6−2=x

⇒4=x

∴ The number is 64.

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Answer 2

Answer:

Let x = ones digit

and y = tens digit

then from "a two digit number is 4 more than six times the sum of its digits":

x + 10y = 6(x+y)+4

x + 10y = 6x+6y+4

10y = 5x+6y+4

4y = 5x+4

.

and, from "if 18 is subtracted from the number,the digits are reversed.find the number"

x+10y -18 = y+10x

10y -18 = y+9x

9y -18 = 9x

y -2 = x

.

substitute the above into:

4y = 5x+4

4y = 5(y-2)+4

4y = 5y-10+4

4y = 5y-6

4y+6 = 5y

6 = y

.

substitute above into:

4y = 5x+4

4(6) = 5x+4

24 = 5x+4

20 = 5x

4 = x

.

The number is 64

Step-by-step explanation:

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