|
Question 561655: the sum of the digits of a 3-digit number is 14. the hundred's digit being four times the unit's digit. if 594 is subtracted from the number, the number will be reversed.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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 sum of the digits of a 3-digit number is 14."
a + b + c = 14
:
"the hundred's digit being four times the unit's digit."
a = 4c
:
" if 594 is subtracted from the number, the number will be reversed."
100a + 10b + c - 594 = 100c + 10b + a
100a - a + 10b - 10b = 100c - c + 594
99a = 99c + 594
simplify, divide by 99
a = c + 6
replace a with 4c
4c = c + 6
4c - c = 6
3c = 6
c = 2 is the units
then
a = 4(2)
a = 8 is the 100's
:
then
b = 14 - 2 - 8
b = 4 is 10s
:
842 is the number
:
:
See if that works in the statement:
"if 594 is subtracted from the number, the number will be reversed."
842 - 594 = 248
248 = 248
|
|
|
| |
