Question

Four times the sum of the digits of a two digit number is 18 less than the number and is also 9 less than the number formed by reversing its digits. Find the product of its digits

Answer 1

Answer:let the two digits of a two digit number be X and Y.

Then the two digit number so formed is (10x+y),where X is at 10's place and Y is at unit place.

By question,

4 (X+y)=(10x+y)-18............(1)

And

4(X+y)=(10y+X)-9..............(2)

From above two equations we have,

10x+y-18=10y+x-9

Or,9x-9y-9=0

Or,x-y-1=0

Or,X=(1+y)

Using this value of X in (1) we get

4(1+y+y)=10(1+y)+y-18

Or,4+8y=10+11y-18

Or,12=3y

Therefore,y=4

Now X=(1+y)=1+4=5

Now required product of digits is

X*y=5*4= 20

Step-by-step explanation:

Answer 2

Answer with Step by step explanation:

Four times the sum of the digits of a two-digit number is equal to the number.

It the digits are reversed, the resulting number is 27 greater than the original number.

What is the number?

:

Let x = the 10's digit

Let y = the units digit

then

10x + y = "the number"

:

Write an equation for each statement:

:

"Four times the sum of the digits of a two-digit number is equal to the number."

4(x+y) = 10x + y

4x + 4y = 10x + y

4y - y = 10x - 4x

3y = 6x

Simplify, divide by 3

y = 2x

:

"If the digits are reversed, the resulting number is 27 greater than the original number."

10y + x = 10x + y + 27

10y - y = 10x - x + 27

9y = 9x + 27

Simplify divide by 9

y = x + 3

:

From the 1st statement equation, replace y with 2x

2x = x + 3

2x - x = 3

x = 3

then

y = 2(3)

y = 6

:

36 = " the number"

:

:

Check solutions in the statement:

"If the digits are reversed, the resulting number is 27 greater than the original number."

63 = 36 + 27

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