Question

The sum of 5 consecutive integers is 75 find the smallest of these number

Answer 1

They are centered around 75, so without doing any algebra we can say the numbers are 73, 74, 75, 76, 77; the least and greatest numbers are 73 and 77

Please mark as brain list

Answer 2

Let the common multiple be x

So, let the five consecutive integers be x, x + 1, x + 2, x + 3 and x + 4

Their sum is 75


According to the given condition

x + x + 1 + x + 2 + x + 3 + x + 4 = 75

Add the like terms

☛ 5x + 10 = 75

Move constant +10 to RHS

☛ 5x = 75 - 10

Subtract

☛ 5x = 65

Divide both the sides by 5

∴ x = 13


∴ The smallest number ☛ x

☛ $\large{\boxed{\boxed{\rm{13}}}}$