Question

Three consecutive integers are such they are taken in increasing order and multiplied by 2,3 and 4 respectively. They add up to 56.Find this number

Answer 1

Answer:

y=5

Step-by-step explanation:

The 3 consecutive numbers are y,y+1,y+2

We multiply them by 2,3,4 resp. (given)

y x 2 =2y

(y+1) x 3= 3y + 3

(y+2) x 4=4y + 8

y+(y+1)+(y+2) = 56

i.e. 2y+3y+3+4y+8=56

9y+11=56

9y=45

y=5

therefore the number is 5

Answer 2

Given :-

• When the three consecutive integers are taken in their increasing order multiplied by 2, 3 & 4 respectively, their sum will be 56.

To Find :-

• The three consecutive integers.

Solution :-

Let the three consecutive integers be:-

• x
• x + 1
• x + 2

According to the question,

$\implies\rm{2(x)+3(x+1)+4(x+2)=56}$

$\implies\rm{2x+3x+3+4x+8=56}$

$\implies\rm{9x+11=56}$

$\implies\rm{9x=56-11}$

$\implies\rm{9x=45}$

$\implies\rm{x=\dfrac{45}{9}}$

$\implies\rm{x=}\:\bold{5}$

Hence, the three consecutive integers are:-

• 5 (x)
• 6 (x + 1)
• 7 (x + 2)