At the school sports day each house scores 5 points for winning an event and 2 points for coming second. Falcon House won \(w\) events and came second in 6 ...
Question 1 Report
At the school sports day each house scores 5 points for winning an event and 2 points for coming second. Falcon House won \(w\) events and came second in 6 events. By the end of the day Falcon House had 47 points and no other scores.
- Write down an equation in \(w\). (2)
- Solve your equation to find the number of events Falcon House won. (2)
Answer Details
This question turns a scoring rule into a linear equation. The total score is built from two separate sources, so each one is written as (points per event) × (number of events) before they are added.
(a) Equation in \(w\). [2]
Falcon House won \(w\) events at 5 points each, giving \(5w\) points, and came second in 6 events at 2 points each, giving \(2 \times 6 = 12\) points. The two together make 47 points:
One mark for the \(5w\) term, one for adding the 12 and equating to 47. The statement "no other scores" is what allows the two contributions to be the whole total.
(b) Number of events won. [2]
Subtract the fixed 12 points, then divide by the 5 points per win:
Falcon House won 7 events. Check by substituting: \(5 \times 7 + 12 = 35 + 12 = 47\) points, which matches. One mark for \(5w = 35\), one for \(w = 7\).
Examination point: undo the operations in reverse order. The equation was built by multiplying by 5 and then adding 12, so it is solved by subtracting 12 and then dividing by 5. Dividing 47 by 5 first is the error the two-step structure is designed to catch.
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