Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 1.8 Junior Find the answer

At the Lacsap Hospital, Emily is a doctor and Robert is a nurse. Not including Emily, there are five doctors and three nurses at the hospital. Not including Robert, there are $d$ doctors and $n$ nurses at the hospital. What is the product of $d$ and $n$ ?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

Since Emily is a doctor and there are 5 doctors and 3 nurses aside from Emily at the hospital, then there are 6 doctors and 3 nurses in total. Since Robert is a nurse, then aside from Robert, there are 6 doctors and 2 nurses. Therefore, $d=6$ and $n=2$ , so $dn=12$ .

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