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?

ghistory Jun 12, 2024

#1**+1 **

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! :)

NotThatSmart Jun 12, 2024