KJSEA 2025 Maths Q7 — Inequalities (Number of Learners to Transport)
Published
The Question
“A school must transport x learners. The number of learners is at least 30 but fewer than 50. Which inequality represents this situation, and how is it shown on a number line?”
Translate 'at least 30'
The phrase 'at least 30' means the smallest allowed number is 30 and 30 itself is permitted. Because 30 is included, we use the 'greater than or equal to' sign rather than a strict 'greater than'.
'At least' always includes the boundary value, so the equals part of the sign is kept.
Translate 'fewer than 50'
The phrase 'fewer than 50' means the number can get close to 50 but 50 itself is not allowed. Since 50 is excluded, we use a strict 'less than' sign with no equals part.
Combine into one compound inequality
Both conditions must be true at the same time, so we join them into a single statement with x in the middle. We write the smaller boundary on the left and the larger boundary on the right, keeping each sign as decided above.
Show it on the number line
A solid (filled) dot at 30 shows that 30 is included, while an open circle at 50 shows that 50 is not included. The whole segment between the two marks is shaded to show every allowed value in that range.
Solid dot = value included; open circle = value excluded.
Final Result
The inequality is 30 is less than or equal to x, which is less than 50, written as 30 ≤ x < 50. This is option D.
Why this method works
Word problems about limits translate directly into inequality signs by asking whether each boundary value is itself allowed. 'At least 30' keeps 30 in the range, so the boundary is closed and needs the equals part of the sign; 'fewer than 50' throws 50 out, so that boundary is open. Combining both conditions places x between them, and because each condition must hold simultaneously the result is one compound inequality rather than two separate ones. The number line simply pictures this: a filled dot marks an included boundary and an open circle marks an excluded one.
Test values: 30 works (30 ≤ 30 < 50), 49 works, but 29 fails the lower bound and 50 fails the upper bound — exactly matching 'at least 30 but fewer than 50'.