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Question 323360: four times the sum of the digits of two- digit number is equal to the number. if 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! Let the two digit be x and y
then
10x + y = "the number"
and
10y + x = "the reversed number
:
Write an equation for each statement, simplify the equation:
:
"four times the sum of the digits of two- digit number is equal to the number."
4(x + y) = 10x + y
4x + 4y = 10x + y
4y - y = 10x - 4x
3y = 6x
divide both sides by 3
y = 2x
:
"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
:
what is the number
replace y with 2x, find x
2x = x + 3
2x - x = 3
x = 3 is the 1st digit
and
y = 2(3)
y = 6
:
36 is the original number
:
:
Check solutions in the statements:
"four times the sum of the digits of two- digit number is equal to the number."
4(3+6) = 36
and
"the digits are reversed, the resulting number is 27 greater than the original number."
63 = 27 + 36
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