SOLUTION: 4 times the sum of the digits of a 2 digit number is equal to the number.If the digits are reversed the resulting number is 27 greater than the original number. what' s the number?

Question 440525: 4 times the sum of the digits of a 2 digit number is equal to the number.If the digits are reversed the resulting number is 27 greater than the original number. what' s the number?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
4 times the sum of the digits of a 2 digit number is equal to the number.
If the digits are reversed the resulting number is 27 greater than the original number. what' s the number?
:
Let x = 10's digit
Let y = units
then
10x+y = the original two digit number
:
Write an equation for each statement:
;
"4 times the sum of the digits of a 2 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, replace y with 2x
2x = x + 3
2x - x = 3
x = 3
Find y
y = 2(3)
y = 6
:
Original number = 36
:
:
Check solution 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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