Question

The sum of the digits in a two digit number is 14. If you reverse and double the original number, and then add the result to the original number, the sum is 222. Find the original number

Answer 1

Answer:

Step-by-step explanation:

Let the two digits be x and y, where x is the tens digit and y is the units (ones) digit.

Then the number is 10x + y.

From the question,

The sum of the digits in a two digit number is 14,

That is, x + y = 14 ....... (1)

Also, from the question,

If you reverse and double the original number, and then add the result to the original number, the sum is 222

If the number is reversed, the new number will be 10y + x; and if this is doubled, we will get 2(10y + x).

Now, if this is added to the original number (10x + y), the sum is 222.

That is,

2(10y + x) + (10x + y) = 222

Then,

20y + 2x + 10x + y = 222

12x + 21y = 222 ........ (2)

Now, we will bring the two equations together and solve simultaneously.

x + y = 14 ....... (1)

12x + 21y = 222 ........ (2)

From equation (1)

x + y = 14

Then, x = 14 - y ...... (3)

Substitute the value of x in equation (3) into equation (2)

12x + 21y = 222

12(14 - y) + 21y = 222

168 - 12y + 21y = 222

168 + 9y = 222

9y = 222 - 168

9y = 54

∴ y = 54/9

y = 6

To determine x, substitute the value of y into equation (3)

x = 14 - y

∴ x = 14 - 6

x = 8

∴ x = 8 and y = 6

Recall that, the two digits are x and y, where x is the tens digit and y is the units (ones) digit.

Hence, the original number is 86.