Question 360239: For a certain 3-digit number, interchanging the first and last digits gives a 3-digit number 297 less than the original number. Doubling the first and last digits of the original number gives a 3-digit number and increases the sum of the digits to 15 what is the number?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Let 100x + 10y + z = a three digit number
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Write an equation for each statement:
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For a certain 3-digit number, interchanging the first and last digits gives
a 3-digit number 297 less than the original number.
100x + 10y + z = 100z + 10y + x + 297
100x - x + 10y - 10y = 100z - z + 297
99x = 99z + 297
Simplify, divide thru by 99
x = z + 3
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Doubling the first and last digits of the original number gives a 3-digit
number and increases the sum of the digits to 15
2x + y + 2z = 15
Replace x with (z+3)
2(z+3) + y + 2z = 15
2z + 6 + y + 2z = 15
4z + y = 15 - 6
4z + y = 9
y = -4z + 9
only two positive integer solutions here
z=1, y=5, then x=4
451 is the number
and
z=2, y=1, then x=5
512 is the number, however, it says:
"Doubling the first and last digits gives a 3-digit number", so it can,t be 512
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what is the number? 451
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Check:
451 - 154 = 297
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