Question

A two digit number is four more than six times the sum of its digits.If 18 is subtracted from the number the digits are reversed.Find the number.​

Answer 1

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

Please mark it as brainlist

Answer 2

Step-by-step explanation:

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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