Question

Find three consecutive positive integers whose sum is 30​

Answer 1

Answer:

Step-by-step explanation:

Let the three consecutive positive integers are x , x + 1 and x + 3.

Their sum = 30

x + x + 1 + x + 2 = 30

3x + 3 = 30

3x = 30 - 3

3x = 27

x = 27 / 3

x = 9.

There,the the three consecutive integers are

x , x + 1 , and x + 3

= 9, 9+1 and 9+3

= 9, 10 and 12 is the answer.

Answer 2

$\Huge\texttt{9, 10, 11}$

$\huge\texttt{\underline{\underline{Preview}}}$

A linear equation problem with the idea of consecutive numbers

$\large\texttt{\underline{Three consecutive numbers}}$

Consecutive numbers have the same amount of increase.

$\bullet\ (n-1),\ n,\ (n+1)\ \texttt{(Odd consecutive numbers)}$

$\cdots\longrightarrow\texttt{The sum of }\underline{\underline{3n}}$

$\bullet\ \left(n-\dfrac{3}{2}\right),\ \left(n-\dfrac{1}{2}\right),\ \left(n+\dfrac{1}{2}\right), \left(n+\dfrac{3}{2}\right)\ \texttt{(Even consecutive numbers)}$

$\cdots\longrightarrow\texttt{The sum of }\underline{\underline{4n}}$

Even consecutive numbers contain fractions because numbers leave no constant terms in the sum.

$\large\texttt{\underline{Linear equations}}$

Adding/subtracting/multiplying the same numbers on both sides keeps it true.

$\cdots\longrightarrow ax+b=0\ (a\neq0)$

$\cdots\longrightarrow ax=-b\ \texttt{(Isolation)}$

$\cdots\longrightarrow x=-\dfrac{b}{a}\ \texttt{(Division)}$

$\huge\texttt{\underline{\underline{Explanation}}}$

Three consecutive numbers are $n-1,\ n,\ n+1$.

$\cdots\longrightarrow (n-1)+n+(n+1)=30$

Collecting like terms

$\cdots\longrightarrow 3n=30$

By dividing both sides by 3

$\cdots\longrightarrow n=10$

Hence, -

$\bullet\texttt{ 9, 10, 11 (Answer)}$

$\huge\texttt{\underline{\underline{Shortcut trick}}}$

The average of consecutive numbers is the median.

$\cdots\longrightarrow n=10$

Hence, -

$\bullet\texttt{ 9, 10, 11 (Answer)}$