Sports day organisers must set out enough chairs for 160 spectators. Each row holds exactly 14 chairs, where \(r\) is the number of rows used. Form an inequ...
Question 1 Report
Sports day organisers must set out enough chairs for 160 spectators. Each row holds exactly 14 chairs, where \(r\) is the number of rows used.
- Form an inequality in \(r\) using the number of spectators. (2)
- Solve to find the minimum whole number of rows needed. (2)
- Work out how many spare chairs there will be with this number of rows. (1)
Answer Details
Fitting a fixed number of spectators into equal-sized rows means the total seats provided must be at least the number of spectators, which sets up an inequality that is then solved for the least sufficient number of rows.
(a) Each row seats 14 people, and \(r\) rows must seat at least 160 spectators: \(14r \geqslant 160\). [2 marks]
(b) Dividing both sides by \(14\): \(r \geqslant 11.43\) (to 2 decimal places). Since \(r\) must be a whole number and rows cannot be partially used, the minimum whole number of rows is \(12\). [2 marks]
(c) With \(12\) rows, the total number of chairs is \(14 \times 12 = 168\), leaving \(168 - 160 = 8\) spare chairs. [1 mark]
Rounding \(11.43\) up (not down) to \(12\) is essential here: \(11\) rows would only seat \(154\) people, which is fewer than the \(160\) spectators who need a seat.
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