Question

the middle digit of a three digit number is half the sum of the other two digits.the number is 20.5 times the sum of the digits.the new number obtained by interchanging the digits is the units place and hundred's place is more than original number by 594.find the original number​

Answer 1

6464946.45649ok jsjaok

Answer 2

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Answer:

369, 258, 147

Step-by-step explanation:

let a = 100's digit

let b = the 10's

let c = the units

then

100a+10b+c = the original number

Write an equation for each statement, simplify as much as possible

the middle digit of a three digit number is half the sum of the other two digits.

b = 5(a+c)

b = 5a + 5c

The number is 20.5 times the sum of its digits.

100a+10b+c = 20.5(a+b+c)

The new number obtained by interchanging the digits in the unit's and hundred's places is more than the original number by 594.

100a + 10b + c + 594 = 100c + 10b + a

100a - a + 10b - 10b = 100c - c - 594

99a = 99c - 594

simplify, divide by 99

a = c - 6

We know that c has to be 7, 8, or 9

in the first equation, b = 5a + 5c, replace a with (c+6)

b = 5(c-6) + 5c

b = 5c - 3 + 5c

b = c - 3

if c = 9, then the number is 369

if c = 8, then the number is 258

if c = 7, then the number is 147

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