Question 186852
the tens digit of a two-digit number exceeds twice the units digit by 1.
 if the digits are reversed, the sum of the new number and the original
 number is 143. find the original number.
:
Let x = the 10's digit
Let y = the units
then
10x + y = the number
:
"the tens digit of a two-digit number exceeds twice the units digit by 1."
x = 2y + 1
or
x - 2y = 1
:
"if the digits are reversed, the sum of the new number and the original number is 143."
(10y + x) + (10x + y) = 143
10y + x + 10x + y = 143
11x + 11y = 143
Simplify, divide equation by 11
x + y = 13
:
Subtract the 1st equation
x + y = 13
x - 2y = 1
-------------eliminates x
0x + 3y = 12
y = 4
then
x = 2(4) + 1
x = 9
;
94 = the number
:
:
Check solution in the statement:
if the digits are reversed, the sum of the new number and the original number is 143.
49 + 94 = 143