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

Answer:

The three consecutive integers are 7,8 and 9.

Step-by-step explanation:

Let the three integers be x, y and z in increasing order.

Given that, the integers are three consecutive integers,

therefore, y = x + 1  and  z = x + 2 ------- (1)

Now, (x * 2) + (y * 3) + (z * 4) = 74 ------- (2)

Substituting values of y and z from (1) in (2),

(x * 2) + [(x + 1) * 3] + [(x + 2) * 4] = 74

=> (2x) + (3x + 3) + (4x + 8) = 74

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

=> 9x + 11 = 74

=> 9x = 74 - 11

=> 9x = 63

=> x = 63/9

=>  x = 7

Now , substiuting x = 7 in (1),

y = x + 1 = 7 + 1 = 8

z = x + 2 = 7 + 2 = 9

Therefore, the three consecutive integers are 7, 8 and 9.

CROSS CHECK

(7*2) + (8*3) + (9*4) = 14 + 24 + 36 = 74

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