SOLUTION: When a certain three digit number is divided by the number with digits reversed, the quotient is 2 and the remainder is 25. The tens digit is one less than twice the sum of the hun

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Question 521532: When a certain three digit number is divided by the number with digits reversed, the quotient is 2 and the remainder is 25. The tens digit is one less than twice the sum of the hundreds digits and units digit. If the units digit is subtracted from the tens digit, the result is twice the hundreds digits. Find the number.
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:
:
"When a certain three digit number is divided by the number with digits reversed, the quotient is 2 and the remainder is 25."
= 2 +
multiply thru by 100c+10b+a, results get rid of the denominators:
100a+10b+c = 2(100c+10b+a) + 25
:
100a + 10b + c = 200c + 20b + 2a + 25
Combine like terms
100a - 2a = 200c - c + 20b - 10b + 25
:
98a = 199c + 10b + 25
:
:
" The tens digit is one less than twice the sum of the hundreds digits and units digit."
b = 2(a+c) - 1
b = 2a + 2c - 1
:
" If the units digit is subtracted from the tens digit, the result is twice the hundreds digits."
b - c = 2a
b = c + 2a
:
b=b, therefore
2a + 2c - 1 = c + 2a
Subtract 2a from both sides:
2c - 1 = c
2c - c = 1
c = 1
:
The 1st equation simplified
98a = 199c + 10b + 25
replace c with 1, in both equations
98a = 199 + 10b + 25
98a = 10b + 224
:
b = 2a + c
b = (2a+1)
:
98a = 10b + 224
substitute for b
98a = 10(2a+1) + 224
98a = 20a + 10 + 224
98a - 20a = 234
78a = 234
a = 234/78
a = 3
:
Find b
b = 2a + c
b = 2(3) + 1
b = 7
then
371 is the number!
:
:
Check this in the 1st statement:
= 2 +