# A2-digit number is such that the ones digit is twice the tens digit. if the digits are interchanged, half the new number is less than the original number by 3. what is the original number?

Answers: 1

## Answers

A2-digit number is such that the ones digit is twice the tens digit. if the digits are interchanged,...

The original number is 24.

Step-by-step explanation:

Let x be the tens digit.

Let y be the ones digit.

{ y= 2x

{ (10y + x) / 2 = (10x + y) - 3

(20x + x) / 2 = 12x - 3

20x + x = 24x - 6

21x = 24x - 6

3x = 6

x = 2

y = 2(2)

y = 4

Original Number: 24

Step-by-step explanation:

Twenty-four meets the criteria to be the original number.

Its ones digit (4) is twice the tens digit (2).When interchanged, the new number is 42. Its half is 3 less than the original number.#answerForTrees

we can substitute the digits to variables such that: x=tens digit ; and y=ones digit. If the two digits were in the same number, then 10x+y. What we know is that the once digit is twice the tens, meaning y=2x. If the number is 10x+y, then the reverse is 10y+x.

10x+y-3 = 1/2(10y+x) ; substitute y as the 2x

10x+(2x)-3 = 1/2(10(2x)+x)

12x-3 = 1/2(21x)

12x-3 = 21x/2 ; multiply both sides by 2 to cancel the fraction

24x-6 = 21x ; combine like terms

3x = 6 ; divide by 3 to remove the constant of variable x

x = 2

Therefore, the tens digit is 2; if twice the tens digit is the ones digit (y=2x), then twice 2 is 4. The digit is 24

#answerfortrees