Question

the sum of three consecutive numbers is 63. find the numbers. the sum of 2 consecutive numbers is 21. find the no.​

Answer 1

Given:-

Sum of three consecutive numbers is 63

To Find:-

The three consecutive numbers

Solution:-

Let the three consecutive numbers be.

x+x+1+x+2=63

Separating likes terms from unlike terms.

3x+3=63

3x=63-3

3x=60

x=60÷3

x=20

1st number :- x=20

2nd number :- x+1= 20+1= 21

3rd number :- x+2= 20+2= 22

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Given:-

Sum of two consecutive numbers is 21

To find:-

The sum of two consecutive numbers

Solution:-

Let the two consecutive numbers be

x+x+1=21

2x+1=21

2x=21-1

2x=20

x=20÷2

x=10

1st number :- x= 10

2nd number :- x+1= 10+1= 11

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Answer 2

Step-by-step explanation:

First question:-

$\frak Given = \begin{cases} &\sf{The\ sum\ of\ three\ consecutive} \\ &\sf{numbers\ is\ 63.} \end{cases}$

To find:- We have to find the numbers ?

☯️ Let the three consecutive numbers be x, x + 1, and x + 2.

__________________

$\frak{\underline{\underline{\dag By\ substituting\ the\ values,\ we\ get:-}}}$

$\sf : \implies {x\ +\ x\ +\ 1\ x\ +\ 2\ =\ 63} \\ \\ \sf : \implies {3x\ +\ 3\ =\ 63} \\ \\ \sf : \implies {3x\ =\ 63\ -\ 3} \\ \\ \sf : \implies {3x\ =\ 60} \\ \\ \sf : \implies {x\ =\ \cancel \dfrac{60}{3}} \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf x\ =\ 20.}}}}\bigstar$

● The value of x is 20.

So here:-

$\sf : \implies {First\ number\ =\ x\ =\ 20.}$

$\sf : \implies {Second\ number\ =\ x\ +\ 1\ =\ 20\ +\ 1\ =\ 21.}$

$\sf : \implies {Third\ number\ =\ x\ +\ 2\ =\ 20\ +\ 2\ =\ 22.}$

$\sf \therefore {\underline{Hence,\ the\ required\ numbers\ are\ 20,\ 21,\ and\ 22.}}$

Second question:-

$\frak Given = \begin{cases} &\sf{The\ sum\ of\ two\ consecutive} \\ &\sf{numbers\ is\ 21.} \end{cases}$

To find:- We have to find the numbers ?

☯️ Let the two consecutive numbers be x, x + 1.

__________________

$\frak{\underline{\underline{\dag By\ substituting\ the\ values,\ we\ get:-}}}$

$\sf : \implies {x\ +\ x\ +\ 1\ =\ 21} \\ \\ \sf : \implies {2x\ +\ 1\ =\ 21} \\ \\ \sf : \implies {2x\ =\ 21\ -\ 1} \\ \\ \sf : \implies {2x\ =\ 20} \\ \\ \sf : \implies {x\ =\ \cancel \dfrac{20}{2}} \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf x\ =\ 10.}}}}\bigstar$

● The value of x is 10.

So here:-

$\sf : \implies {First\ number\ =\ x\ =\ 10.}$

$\sf : \implies {Second\ number\ =\ x\ +\ 1\ =\ 10\ +\ 1\ =\ 11.}$

$\sf \therefore {\underline{Hence,\ the\ required\ numbers\ are\ 10\ and\ 11.}}$