Question 203995: Four times the sum of the digits of a two-digit number is equal to the number. It the digits are reversed, the resulting number is 27 greater than the original number. What is the number?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Four times the sum of the digits of a two-digit number is equal to the number.
It the digits are reversed, the resulting number is 27 greater than the original number.
What is the number?
:
Let x = the 10's digit
Let y = the units digit
then
10x + y = "the number"
:
Write an equation for each statement:
:
"Four times the sum of the digits of a two-digit number is equal to the number."
4(x+y) = 10x + y
4x + 4y = 10x + y
4y - y = 10x - 4x
3y = 6x
Simplify, divide by 3
y = 2x
:
"If the digits are reversed, the resulting number is 27 greater than the original number."
10y + x = 10x + y + 27
10y - y = 10x - x + 27
9y = 9x + 27
Simplify divide by 9
y = x + 3
:
From the 1st statement equation, replace y with 2x
2x = x + 3
2x - x = 3
x = 3
then
y = 2(3)
y = 6
:
36 = " the number"
:
:
Check solutions in the statement:
"If the digits are reversed, the resulting number is 27 greater than the original number."
63 = 36 + 27
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