Mr$.$ Frost controls proxies for $32,000$ of the $60,000$ outstanding shares of Express Frozen

Foods Inc. Mr$.$ Cooke heads a dissident group that controls the remaining $28,000$ shares.

There are seven board members to be elected and cumulative voting applies. Frost does not

understand the cumulative voting and plans to cast $90,000$ of his $224,000$ votes for his brother,

Jack. His remaining votes will be spread evenly for three other candidates.

How many directors can Cooke elect if Frost acts as described above? Use logical numerical

analysis rather than a set formula to answer the question.