Question

Three whole numbers have a total of 100

The first number is a multiple of 15

The second number is ten times the third number

Work out the three numbers

Answer 1

First Number = 45

Second Number = 50

Third Number = 5

Answer 2

Let a be the first, b be second and c be the third whole number.

Since the sum of these three numbers is 100.

So,
`a+b+c=100` (equation 1)

Since, The first number is a multiple of 15

Therefore, a = 15n

And, the second number is ten times the third number.

b = 10c

Substituting the values of 'a' and 'b' in equation 1

So,
`15n+10c+c=100`

`15n+11c = 100`

`11c = 100-15n`

`c=(100-15n)/(11)`

Therefore, 100-15n should be exactly divisible by 11.

So, by taking n= 1 and 2, 100-15n is not divisible by 11

Let n =3

`c=(100-15 * 3)/(11)`

c= 5

Now, second number (b)= 10c =
`10 * 5= 50`

As, a+b+c=100

a+50+5=100

a+55=100

a=45

Therefore, the three whole numbers are 45,50,5.