+4 Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to \(\frac{21}{4}\) times the largest of the seven integers. What is the smallest integer that Pearl wrote down?
+947
Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 21 / 4 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?
Let the first integer be represented by x.
Since the integers are consecutive, each following
integer is one more than the integer before it.
(x) + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) = (21/4) • (x + 6)
21x + 126
7x + 21 = –––––––––
4
Multiply both sides by 4
28x + 84 = 21x + 126
Subtract 21x from both sides
7x + 84 = 126
Subtract 84 from both sides
7x = 42
Divide both sides by 7
x = 6
check answer
6 + 7 + 8 + 9 + 10 + 11 + 12 = (21/4)(12)
63 = 63
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