Question & Answer
QUESTION

Of the three consecutive natural numbers, five times the smallest number is 9 more than four times the greatest number, find the numbers.

ANSWER Verified Verified
Hint: In this question first of all consider the smallest natural number as a variable. Then add one to it to get the second consecutive natural number and then add two to the smallest natural number that we considered to get the third consecutive natural number.

Complete step-by-step answer:
Let the three consecutive natural numbers are \[x,x + 1,x + 2\]
Here greatest number \[ = x + 2\]
Middle number \[ = x + 1\]
And smallest number \[ = x\]
Given that, five times the smallest number is 9 more than four times the greatest number.
So, we have
\[
   \Rightarrow 5x = 4\left( {x + 2} \right) + 9 \\
   \Rightarrow 5x = 4x + 8 + 9 \\
   \Rightarrow 5x - 4x = 17 \\
  \therefore x = 17 \\
\]
Thus, we have
\[
   \Rightarrow x = 17 \\
   \Rightarrow x + 1 = 17 + 1 = 18 \\
   \Rightarrow x + 2 = 17 + 2 = 19 \\
\]
Therefore, the consecutive three natural numbers are 17, 18 and 19.

Note: Here the considered variable \[x\] is also a natural number. We can verify our answer by substituting \[x = 17\] in the equation \[5x = 4\left( {x + 2} \right) + 9\] which is our given condition. We can assume the greatest number as variable x then also we will get the same result.