Answer:
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.