Asked by Peter
A three digit number is such that twice the hundreds digit is more the teens digit by two.The unit digit is thrice the hundreds digit.When the digits are reversed the number is increased by 594.Find the number ?
Answers
Answered by
Reiny
hundred digit --- a
tens digit ---- b
unit digit --- c
original number: 100a + 10b + c
number reversed : 100c + 10b + c
100c + 10b + a - (100a + 10b + c) = 594
99c - 99a = 594
c - a = 6
"the unit digit is thrice the hundreds digit" -----> c = 3a
3a -a = 6
a = 3
then c = 9
"twice the hundreds digit is more the teens digit by two" ----> b = 4
<b>your number is 349</b>
check:
943 - 349 = 594
tens digit ---- b
unit digit --- c
original number: 100a + 10b + c
number reversed : 100c + 10b + c
100c + 10b + a - (100a + 10b + c) = 594
99c - 99a = 594
c - a = 6
"the unit digit is thrice the hundreds digit" -----> c = 3a
3a -a = 6
a = 3
then c = 9
"twice the hundreds digit is more the teens digit by two" ----> b = 4
<b>your number is 349</b>
check:
943 - 349 = 594
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