Problem 5.3. Irina did poorly in math at the beginning of the school year, so she had 3 threes and 2 twos in her journal. But in mid-October, she pulled herself together and started getting only fives. What is the minimum number of fives Irina needs to get so that her average grade is exactly 4?
Answer: 7.

Solution. Let Irina need to get $x$ fives. Then the sum of her grades will be $3 \cdot 3+2 \cdot 2+5 x=5 x+13$, and the number of grades $-3+2+x=x+5$.

We get the equation

$$
\begin{aligned}
(5 x+13) & :(x+5)=4 \\
5 x+13 & =4(x+5) \\
5 x+13 & =4 x+20 \\
x & =7
\end{aligned}
$$