Question

the sum of the digits of a number consisting of three digits is 12, the middle digit is equal to half the sum of the other two. If the order of the digits is reversed, the number is diminished by 198. Find the number

Answer 1

543

Let a, b, c = the three digits

then

100a+10b+c = "the number"

:

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

:

the sum of the digits of a number consisting of three digit is 12.

a + b + c = 12

:

he middle digit is equal to half of the sum of the other two.

b = .5(a+c)

:

if the order of the digit be reversed the number is diminished by 198 find be number

100c + 10b + a = 100a + 10b + c - 198

100c - c + 10b - 10b = 100a - a - 198

99c = 99a - 198

simplify, divide by 99

c = a - 2

:

In the 2nd equation, b = .5(a+c), replace c with (a-2)

b = .5(a + a - 2)

b = .5(2a-2)

b = a - 1

:

In the 1st equation replace b with (a-1); replace c with (a-2)

a + (a-1) + (a-2) = 12

3a - 3 = 12

3a = 12 + 3

a = 15/3

a = 5

then using the above equations we know that:

b = 4

and

c = 3

:

543 is the number

:

:

Check that in the last statement

345 = 543 - 198