Question

If product of four consecutive positive integers is 1680,then find the numbers.

Answer 1

Product of the 4 consecutive number is 1680

1st Step: Let's get an estimate of the number:

Let the average of the 4 numbers be x

x⁴ = 1680

x = 6.4

⇒ These are 4 consecutive numbers, therefore the average number is one that is between the 2nd and the 3rd number.

2nd Step: Find the 4 numbers:

⇒ These are 4 consecutive numbers, therefore the average number is one that is between the 2nd and the 3rd number.

⇒ It is a reasonable guess to say that the 2nd number is 6 and the third number is 7. Therefore the first number is 5 and the last number is 8.

Guess: The numbers are 5,6,7 and 8

Check: 5 x 6 x 7 x 8 = 1680 (Verified)

Answer: The numbers are 5, 6, 7 and 8

Answer 2

Let the four consecutive numbers be :- x , x+1 , x+2 , x+3.

According to question -----

=> x + x + 1 + x + 2 + x + 3 = 1680
=> 4x + 6 = 1680
=> 4x = 1680 - 6
=> 4x = 1674
=> x = 1674 ÷ 4
=> x = 418.5

x+1 = 418.5 + 1 => 419.5

x + 2 = 418.5 + 2 => 420.5

x + 3 = 418.5 + 3 => 421.5

HOPE IT HELPS YOU...