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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?

 Jun 12, 2024
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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! :)

 Jun 12, 2024

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