Sports day relay batons are shared out so that each house receives at least a quarter of the total number of batons available, \(b\), with a minimum of 9 ba...
Question 1 Report
Sports day relay batons are shared out so that each house receives at least a quarter of the total number of batons available, \(b\), with a minimum of 9 batons per house.
- Solve the inequality \(\dfrac{b}{4} \ge 9\) to find the least number of batons needed. (2)
- Show this solution on the number line below. (1)
Answer Details
Each house's share is at least a quarter of the total batons available; solving the inequality for the total, \(b\), finds the smallest total that guarantees every house gets at least the required minimum of \(9\).
(a) Multiplying both sides of \(\dfrac{b}{4} \geqslant 9\) by \(4\): \(b \geqslant 36\), so the least number of batons needed is \(36\). [2 marks]
(b) Because the inequality is \(\geqslant\) (not strict), the number line shows a closed (filled) circle at \(36\) with an arrow shading all values to the right. [1 mark]
Checking confirms the answer: with exactly \(36\) batons, each house receives \(36 \div 4 = 9\), meeting the minimum requirement exactly.
Download The App On Google Playstore
Everything you need to excel in your exams
