The team wants to win $\frac{3}{4}$ of all their matches in the season. However, in the first third of these matches, they only won $55\%$ of them.

a) What percentage of the remaining matches would the team need to win to achieve their intended goal?

b) If the team won all the remaining matches, what percentage of their matches would they win in the entire season?
a) The team won $\frac{55}{100}$ of a third of the matches, and to win $\frac{3}{4}$ of all matches, they need to win another $p / 100$ of $\frac{2}{3}$ of the matches:

$$
\frac{55}{100} \cdot \frac{1}{3}+\frac{p}{100} \cdot \frac{2}{3}=\frac{3}{4}
$$

From this, we get

$$
p=85
$$

Thus, the team would need to win $85\%$ of the remaining matches.

b) If the team won all the remaining matches, they would win a total of

$$
\frac{55}{100} \cdot \frac{1}{3}+\frac{2}{3}=\frac{255}{300}=\frac{85}{100}
$$

which is $85\%$ of all their matches.

[For each part a), b) award 3 points]