Online accounts with an algebraic frequency

Core stretch

Numbers of accounts 0, 1, 2, 3, 4 have frequencies 5,\(p\), 10, 12, 6. Conditions are independent. Find

1. the greatest integer \(p\) for which 3 is the unique mode,[2]
2. the greatest integer \(p\) for which the median is 2,[3]
3. \(p\) if the mean is \(\frac{87}{40}\).[2]