Sevens
What is the largest number Sophie can use to have seven positive integers with a mean of 7?
Age
11 to 14
Challenge level
Problem
Sophie has to choose seven different positive (non zero) whole numbers whose mean is 7.
What is the largest possible number that she could choose as one of the seven numbers?
Student Solutions
If there are seven numbers that have a mean of $7$, then: $$\frac{\text{Total}}{7} = 7$$
This means that the total of the numbers is $7 \times 7 = 49$.
The smallest that the first six numbers could be is $1$, $2$, $3$, $4$, $5$ and $6$.
These have a total of $21$.
This means the largest that the seventh number could be is $49 - 21 = 28$.