The average of 7 cons. integers is 10. What are they?

[ronhongxo]

1. The average of seven consecutive integers is 10. What are the seven integers?

2. The average of five integers is 25. If two of the integers are 10 and 19 and the others are three consecutive integers, determine these three integers.

Thank you for your help!

 

[stapel]

Think: How do you find the average of a list of numbers?

1) If the average of the seven numbers is ten, then what is their sum? If the integers are "consecutive", then you have the middle number (let's call it "m"), with three numbers less and three numbers more. In fact, the three that are less are less by exactly the same amount that the other three are more. So how do the numbers relate to "m"? How does this allow you to find "m", and then the others?

2) If the average is 25, then what is the sum? If two of the numbers are 10 and 19, what is the sum of the remaining three? Then what is the middle of those three numbers? Then what are the other two numbers?

If you get stuck, or are unsure of your steps or your solutions, please reply showing how far you have gotten. Thank you.

Eliz.