Chapter 1.5, Problem 21STP

To determine

What is the sum of three whole numbers.

Answer to Problem 21STP

  $\begin{array}{l}5,6,7\\ 5+6+7=18\end{array}$

Explanation of Solution

In order to find what is the sum of three whole numbers, first let the number be $x,x+1,x+2$ ,so it can written as :

  $x\left(x+1\right)\left(x+2\right)=210$

210 is divisible by 2 but not by 4 so the three number sequence must be:

Odd, even, odd.

So, we can rewrite the product as

  $\begin{array}{l}x\left(\frac{x+1}{2}\right)\left(x+2\right)=\frac{210}{2}\\ x\left(\frac{x+1}{2}\right)\left(x+2\right)=105\end{array}$

Now, factorise 105, it ends in 5 it must be divisible by 5, giving 5*21.

Factorise 21 giving 7*3.

Re-arrange and the product is 5*3*7.

Since 3=(x+1)/2 we arrive at the required sequence:

  $5\times 6\times 7=210$

So, the sum of the three numbers is $5+6+7=18$ .