+56 Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 28/5 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?
+1790 Let's define some variables to help us solve the problem. Let's set the smallest number as n.
We have \(n + n+1 + n+2 ....... n+6 = 7n + 21\)
Since the sum of the integers add up to 28/5 times the largest number, which is n+6, we can write the equation
\(7n+21=28/5(n+6)\)
Now, we simply solve for n. We get
\(7n+21=\frac{28}{5}n + 168/5\\ 7/5n=63/5\)
Multiplying both sides by 5/7, we get \(n=\frac{63}{5} \cdot \frac{5}{7}=9\)
So our final answer is 9.
Thanks! :)
