Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 6 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?
If we let the smallest integer = x then the sum of all the integers is:
x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 = 6(x+6)
Simplifying we get:
7x + 21 = 6x + 36
x = 15
So the smallest integer is 15.
(Please tell me if this answer is incorrect)