Maths-

General

Easy

Question

# The sum of three consecutive odd integers is 57.What are three integers ?

Hint:

### Integers refer to all whole numbers (Not fractions) and their opposites i.e. all positive numbers, all negative numbers and zero.

Consecutive odd Integers are odd numbers that on a number line come one after another and the difference between each consecutive odd integer is 2.

## The correct answer is: The 3 consecutive odd integers whose sum is 57 are- 17, 19 & 21

### Step-by-step solution:-

Let the 3 consecutive integers be 'x', 'x+2' and 'x+4'.

As per the given condition, the sum of these 3 integers is 57.

∴ Adding the 3 integers, we get-

x + (x+2) + (x+4) = 57

∴ x + x + x = 57 - 2 - 4 ............................................. (Taking all variables and constants on either sides of the equation)

∴ 3x = 51

∴ x = .................................................. (Dividing both sides by 3)

∴ x = 17

∴ First Consecutive odd integer = x = 17 ......................................................... (Equation i)

Substituting the value of x in the other 2 integers, we get-

∴ Second consecutive odd integer = x + 2

∴ Second consecutive odd integer = 17 + 2 ....................................................................... (From Equation i)

∴ Second consecutive odd integer = 19

∴ Third consecutive odd integer = x + 4

∴ Third consecutive odd integer = 17 + 4 ....................................................................... (From Equation i)

∴ Third consecutive odd integer = 21

Final Answer:-

∴ The 3 consecutive odd integers whose sum is 57 are- 17, 19 & 21.

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