Given the average of 15 students, and the average of 10 of them, what's the average of the other 5?

Question

The average value of a diagnostic test from $10$ students is $55$. If we add $5$ more student so the total number of students is $15$, the average value changes to $53$.

How much is the average value from the last $5$ students?

Answer 1

If the average of the the first $10$ students is $55$, then the sum of their total scores is $55 \cdot 10 = 550$. If you add $5$ more students and the average is $53$, then the total would be $$15 \cdot 53=795$$ Subtract $550$ from that to get the total for the $5$ new students, which is $245$. Then, simply divide that by $5$ to get the average, which is $$\dfrac {245}5=49$$

Answer 2

SuomynonA already gave the solution, but I advise to write your problem in equation form to solve it. This is a better and more general way to solve these kind of issues.

The equation for this problem is:

$$10 \times 55 + 5x=15 \times 53$$

Please don't just solve the equation, but have a look why it's build up like this.

Answer 3

Calculate The simply total value of 10 students

$$10×55=550$$

Now, calculate the total value of 15 students,

$$15×53=795$$ Calculate the total value of 5 students, $$795-550=245$$ Calculate the average of 5 students, $$\dfrac{245}{5}=49$$