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Question 481455: a two digit number is 4 times the sum of its digits, if the number is doubled and then decreased by 12, the result is the number with the digits reversed. what is the number?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Let x = the 10's digit, Let y = units
then
10x+y is the two digit number
and
10y+x is the number reversed
:
Write an equation for each statement:
:
"two digit number is 4 times the sum of its digits,"
10x + y = 4(x+y)
10x + y = 4x + 4y
10x - 4x = 4y - y
6x = 3y
Simplify, divide both sides by 2
2x = y
:
"if the number is doubled and then decreased by 12, the result is the number with the digits reversed.
2(10x+y) - 12 = 10y + x
20x + 2y - 12 = 10y + x
20x - x = 10y - 2y + 12
19x = 8y + 12
Replace y with 2x (from the 1st equation)
19x = 8(2x) + 12
19x = 16x + 12
19x - 16x = 12
3x = 12
x = 4 is the 10's digit
and
y = 2(4)
y = 8 is the units
therefore
48 is the number
:
You can confirm this by using 48 as the number in both statements
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