Question

14. Three Consecutive integers add up to 45. What are these integers?
IV. Each Question Carry 4 Marks (Do any 3)​

Answer 1

Answer

• Three consecutive integers are => 14, 15 and 16

To Find

• All the integers.

Given

• Three consecutive integers add up to 45.

Step By Step Explanation

Given that three consecutive integers add up to 45.

Let us consider the integers be ⤵

x, x + 1 and x + 2

Equation ⤵

$\dag{ \boxed {\sf{x + x + 1 + x + 2 = 45}}}$

So let's solve this equation !!

$:\implies \sf \: x + x + 1 + x + 2 = 45 \\ \\ :\implies \sf3x + 3 = 45 \\ \\:\implies \sf 3x = 45 - 3 \\ \\ :\implies \sf 3x = 42 \\ \\ :\implies \sf x = \cancel\cfrac{42}{3} \\ \\ \longmapsto \bf x = 14$

Therefore all the integers are ⤵

x = 14 , x + 1 = 15 and x + 2 = 16

_____________

☆ Proof

L.H.S.

=> 14 + 15 + 16

=> 45

R.H.S.

=> 45

Therefore L.H.S. = R.H.S.

__________________________

Answer 2

Answer:

14, 15, 16

Step-by-step explanation:

14+15+16=45

let the first integer be x

the second number be x+1

and the third number be x+2

now,

x + ( x+1 ) + ( x+2 ) = 45

x + x + 1 + x + 2 = 45

3x + 3 = 45

3x = 45 - 3

3x = 42

x = 42 ÷ 3

x = 14

the first number = x

= 14

the second number= x + 1

= 14 + 1

= 15

the third number = x + 2

= 14 + 2

= 16

hope it helps u