SOLUTION: a number of 3 digits is such hat the tens digit exceeds the unit digit by 2. If this number exceeds the number formed by reversing the digits 297 ad if the sum of its digits is 14,
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Question 698987: a number of 3 digits is such hat the tens digit exceeds the unit digit by 2. If this number exceeds the number formed by reversing the digits 297 ad if the sum of its digits is 14, find the number.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a number of 3 digits is such hat the tens digit exceeds the unit digit by 2.
If this number exceeds the number formed by reversing the digits by 297
and if the sum of its digits is 14, find the number.
:
Let a = the 100's digit
Let b = the 10's digit
Let c = the units
then
100a + 10b + c = "the 3digit number
and
100c + 10b + a = the number reversed
:
" the tens digit exceeds the unit digit by 2."
b = c+2
:
" If this number exceeds the number formed, by reversing the digits by 297"
100a + 10b + c = 100c + 10b + a + 297
Combine like terms
100a - a + 10b - 10b = 100c - c + 297
99a = 99c + 297
Simplify, divide by 99
a = c + 3
:
"the sum of its digits is 14,"
a + b + c = 14
replace a with (c+3), replace b with (c+2)
c + 3 + c + 2 + c = 14
3c + 5 = 14
3c = 14 - 5
c = 9/3
c = 3
:
I'll let you find a and b
check the number you come up with in each statement
:
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