Question

8)The sum of three consecutive integers is 48. Find the 3 integers.​

Answer 1

Answer:

15, 16 & 17

Explanation:

Let the first integer be $x$

According to the question ,

Other two numbers will be $(x + 1)$ and $(x + 2)$ respectively.

$\therefore x + (x + 1) + (x + 2) = 48$

Solving for $\boldsymbol x$

$\implies \: x + x + 1 + x + 2 = 48$

$\implies \: 3x + 3 = 48$

$\implies \: 3x = 48 - 3$

$\implies \: 3x = 45$

$\implies \: x = \dfrac{45}{3}$

$\implies \: x = 15$

$\sf \therefore \: The \: {1}^{st} \: integer \: is \bf \: 15$

Hence, the other two will be :

• $(x + 1) = \bf 16$
• $(x + 2) = \bf 17$

Answer 2

Given : The sum of three consecutive integers is 48.

To Find : Those three integers.

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀____________________

Let those integers be x , (x + 1) and (x + 2) respectively.

$\: \:$

• The sum of all those integers is 48.

$\: \:$

$\sf : \implies \: x + (x + 1) + (x + 2) = 48$

$\: \:$

$\bold{ \underline{According \: to \: question \: : }}$

$\: \:$

$\sf : \implies \: x + (x + 1) + (x + 2) = 48 \\ \\ \\ \sf : \implies \:x + x + 1 + x + 2 = 48 \\ \\ \\ \sf : \implies \:x + x + x + 1 + 2 = 48 \\ \\ \\ \sf : \implies \:3x + 3 = 48 \\ \\ \\ \sf : \implies \:3x = 48 - 3 \\ \\ \\ \sf : \implies \:3x = 45 \\ \\ \\ \sf : \implies \:x = \cancel \frac{45}{3} \\ \\ \\ \sf : \implies \:\underline{\boxed{\mathfrak\purple{x = 15}}} \: \bigstar$

$\: \:$

Now, putting the value of x in the numbers.

$\: \:$

• First consecutive integer = x = 15
• Second consecutive integer = x + 1 = 15 + 1 = 16
• Third consecutive integer = x + 2 = 15 + 2 = 17

$\: \:$

$\sf\therefore{\underline{Hence, \: the \:three \: consecutive \: integers \: are \: \bold{15}, \: \bold{16} \: and \: \bold{17} \: respectively.}}$