SOLUTION: The sum of the digits of a two-digit number is 11. When the digits are reversed, the new number is increased by 20 which is twice the original number. Find the original number.
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Question 150667This question is from textbook
: The sum of the digits of a two-digit number is 11. When the digits are reversed, the new number is increased by 20 which is twice the original number. Find the original number. This question is from textbook
You can put this solution on YOUR website! Let x = the 10's digit
Let y = the units digit
:
the number = (10x + y)
the reversed number = (10y + x)
"
Write an equation for each statement:
"The sum of the digits of a two-digit number is 11."
x + y = 11
or
y = 11-x
:
"When the digits are reversed, the new number is increased by 20 which is twice the original number."
(10y+x) + 20 = 2(10x+y)
10y + x + 20 = 20x + 2y
10y - 2y + x - 20x = -20
8y - 19x = -20
:
Find the original number.
;
Substitute (11-x) for y in the above equation:
8(11-x) - 19x = -20
88 - 8x - 19x = -20
-8x - 19x = 20 - 88
-27x = -108
x =
x = +4
:
y = 11-4
y = 7
:
original number: 47
;
:
Check solution in the statement;
"When the digits are reversed, the new number is increased by 20 which is twice the original number."
74 + 20 = 2(47); confirms our solutions
