Question

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In a two-digit number the tens digit is four less than the units digit. Seven times the tens digit plus five times the units digit is equal to 56. Find the digits.

Answer 1

The digits are 37 (Thirty seven).

Explanation:

Given:

Two digit number.

Let the ones place digit be x

and

The tens place digit be (x - 4)

So the two digit number is (x-4)(x).

According to question:

Seven times the tens digit plus five times the units digit is equal to 56.

⇒
`7(x-4)+5(x)=56`

⇒
`7x-28+5x=56`

⇒
`12x=56+28` ...subtracting 28 both sides

⇒
`12x=84`

⇒
`x=(84)/(12)=7` ...dividing both sides with 12

So the ones place digit is
`x=7` and tens place digit is
`(x-4)=(7-4)=3`

The number is 37.

Check:

`7(x-4)+5(x)=56`

`7(7-4)+5(7)=56`

`21+35=56`

`56=56`

So the digits are 37 as our final answer.