Question

Three consecutive integers are such that when they are taken in increasing order and multiplied by 2,3 and 4 respectively, they add up to 74. Find these numbers

Answer 1

Given :

Three consecutive integers are such that when they are taken in increasing order and multiplied by 2,3 and 4 respectively, they add up to 74.

Solution :

Let us assume the three consecutive integers to be x, x+1 and x+2.

So,

Let us multiply the three integers with 2,3 and 4 respectively,

we get,

⇒ x*2 = 2x

⇒ (x+1)*3 = 3x + 3

⇒ (x+2)*4 = 4x + 8

Now adding 1, 2 and 3 we get ,

2x +3x+3 +4x+8 =74

9x+11 = 74

9x =74-11      

x = 63/9

x = 7

So,

the three integers are,

x=7

x+1 = 8

x+2 = 9

Answer 2

Answer:

7, 8, 9

Step-By-Step Explanation:

Let the three consecutive integers are x, x+1 and x+2.

According to the question,

2x + 3(x+1) + 4(x+2) = 74

⇒ 2x + 3x +3 + 4x + 8 = 74

⇒ 9x + 11 = 74

⇒ 9x = 74 – 11

⇒ 9x = 63

⇒ x = 63/9

⇒ x = 7

Thus, the numbers are:

x = 7

x + 1 = 8

x + 2 = 9