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, $15n+10c+c=100$

$15n+11c = 100$

$11c = 100-15n$

$c=\frac{100-15n}{11}$

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

$c=\frac{100-15 \times 3}{11}$

c= 5

Now, second number (b)= 10c = $10 \times 5= 50$

As, a+b+c=100

a+50+5=100

a+55=100

a=45

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