SOLUTION: The ten's digit of a three-digit number is twice the unit's digit.The hundred's digit of the number is twice the ten's digit. The number formed by reversing the digits of the numb
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Question 836481: The ten's digit of a three-digit number is twice the unit's digit.The hundred's digit of the number is twice the ten's digit. The number formed by reversing the digits of the number is 594 less than it.Find the number. Answer by ankor@dixie-net.com(22740) (Show Source):
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let a = the 100's digit
let b = the 10's
let c = the units
then
100a + 10b + c = "the number"
:
Write an equation for each statement:
The ten's digit of a three-digit number is twice the unit's digit.
b = 2c
or
c = .5b
The hundred's digit of the number is twice the ten's digit.
a = 2b
The number formed by reversing the digits of the number is 594 less than it
100a + 10b + c = 100c + 10b + a + 594
100a - a + 10b - 10b = 100c - c + 594
99a = 99c + 594
simplify, divide by 99
a = c + 6
replace a with 2b, replace c with .5b
2b = .5b + 6
2b - .5b = 6
1.5b = 6
b = 6/1.5
b = 4
then
a = 2(4)
a = 8
and
c = .5(4)
c = 2
:
the number is 842
:
you can check this in the statement:
"The number formed by reversing the digits of the number is 594 less than it"
