How so solve this?
The sum of the digits a two-digit is 12. If the digits are interchanged, 54 increase the number. What is the original number?
Represent the number as xy. That does not mean multiplication; they are positional.
Interchanging the digits, the new number is yx.
y + x = 12
10y + x = 10x + y + 54
9y - 9x = 54
9(y + x) = 12 * 9
9y + 9x = 108 We need the x co-efficients to cancel.
9y - 9x = 54
+(9y + 9x = 108)
--------------------
18y = 162
18y = 162
18y / 18 = 162 / 18
y = 9
9 + x = 12
x = 3
Remember, we represented the number as xy.
The number is 39.
With the digits interchanged, the
new number is 93.
93 - 39 = 54
9 + 3 = 12
It checks.