Question

Solve this question:

The sum of five consecutive integers is 100. Find the five consecutive Integers and next two consecutive integers too.​

Answer 1

$\large{\underline{\mathrm{\red{Question-}}}}$

The sum of five consecutive integers is 100. Find the five consecutive Integers and next two consecutive integers too.

$\large{\underline{\mathrm{\red{Solution-}}}}$

Let the five consecutive integers be x, x+1, x+2, x+3, x+4.

According to the question, sum of these integers is 100.

$\therefore$ (x) + (x+1) + (x+2) + (x+3) + (x+4) = 100....................(1)

: $\implies$ x + x + 1 + x + 2 + x + 3 + x + 4 = 100

: $\implies$ 5x + 10 = 100

: $\implies$ 5x = 100 - 10

: $\implies$ 5x = 90

: $\implies$ x = $\sf{\cancel{\dfrac{90}{5}}}$

$\large{\boxed{\sf{\red{x\:=\:18}}}}$

$\rule{200}2$

★ Five consecutive Integers :

: $\implies$ 18, 19, 20, 21, 22

★ Next two consecutive Integers :

: $\implies$ 23, 24

$\rule{200}2$

Verification:

Put the value of x in (1)

: $\implies$ 18 + 18 + 1 + 18 + 2 + 18 + 3 + 18 + 4 = 100

: $\implies$ 100 = 100

Verified!

Answer 2

Answer:

Let the 5 consecutive numbers be (x-2) ,(x-1), (x),(x+1) ,(x+2)

Sum of all numbers = 100

(x-2)+(x-1)+(x)+(x+1)+(x+2)=100

x-2+x-1+x+x+1+x+2=100

5x=100

x=20

Numbers are as below:

(x-2)=20-2= 18

(x-1)=20-1= 19

x= 20

(x+1)=20+1= 21

(x+2)=20+2=22

“ Numbers are 18,19,20,21 and 22”

Next two consecutive integers are

22+1=23

23+1=24

“Next two consecutive integers are 23 and 24”.