Grouped mean and simultaneous equations

Core stretch

Bukit Merah Secondary School, 2023 Secondary 2 End-of-Year Examination, Mathematics Paper 1, Question 14.

The frequency table shows the number of people who entered a supermarket on a particular weekend.

1. The total frequency is 400.
   Show that \(p+q=120\).[1]
2. The estimated mean age of the visitors is 30.75.
   Show that \(p+3q=252\).[2]
3. Solve the following simultaneous equations.
   \(\begin{aligned}[t]p+q&=120\\p+3q&=252\end{aligned}\)[3]