Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 21 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?
+135 ( I have answered this before )
The smallest integer that Pearl wrote down is 15.
Explanation:
7 consecutive integers. They are:
a
a+1
a+2
a+3
a+4
a+5
a+6
Sum of the integers:
a + a + 1 + a + 2 + a + 3 + a + 4 + a + 5 + a + 6 = 7a + 21
6 times the largest of the seven integers.
The largest is a + 6. So
7a + 21 = 6(a + 6)
7a + 21 = 6a + 36
7a - 6a = 36 - 21
a = 15
The smallest integer that Pearl wrote down is 15.
