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?
+947
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?
Call the smallest integer x. Then each following integer
will be 1 larger than the integer that preceded it.
x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) = 21 • (x + 6)
7x + 21 = 21x + 126
Combine like terms –14x = 105
Divide both sides by –14 x = –7.5
The problem fails already, since 7.5 is not
an integer, whether it's positive or negative. NO SOLUTION
But let's press ahead and see if this would have worked.
Check answer by substituting the value into the problem.
(–7.5) + (–7.5 + 1) + (–7.5 + 2) + (–7.5 + 3) + (–7.5 + 4) + (–7.5 + 5) + (–7.5 + 6) = (21)(–7.5 + 6)
(–7.5) + (–6.5) + (–5.5) + (–4.5) + (–3.5) + (–2.5) + (–1.5) = (21)(1.5)
–31.5 = –31.5
So, –7.5 would have been a good answer IF the problem
had not specified that the numbers have to be integers.
.
