Question

The sum of three positive integers is 18 and their product is 210. If the smallest of the integers is 5, what are the remaining two integers.

Answer 1

The remaining numbers are 7 and 6.

Explanation:

Given:

The sum of three positive integers =18

Their product is 210.

The smallest of the integers is 5

To find:

The other two integers=?

Solution:

Let the other two numbers be a, b

Now,

sum of three numbers = 18

sum of two numbers + 5 = 18

a + b = 18 – 5

a + b = 13.............................. (1)

And, product of 3 numbers = 210

a x b x 5 = 210

a x b = 42................................(2)

Now, as a and b are positive integers a and b values should be lesser than 13 and greater than 5 as given that 5 is the smallest of 3 numbers.

so a x b = 42

a x b = 7 x 6

So, by comparison a = 7 and b = 6.

Let us check it with equation (1)

7 + 6 = 13

13 = 13

Hence, the remaining numbers are 7 and 6.