RV-06-001 · Budget inequalities and admissible whole numbers
A workshop charges a booking fee of £25 plus £3 for each participant. A sponsor will pay only if the total charge is at least £46. The available budget is £130. Write a pair of inequalities for the number n of participants. Find the least and greatest possible whole-number values of n.
Linear Inequalities: Double Constraint & Integer Bounds
Booklet p. 15
Method
1) Write compound inequality: target ≤ fee + cost × n ≤ budget
2) Kill, kill (subtract fee, divide by cost)
3) Pick least and greatest whole numbers
Worked Example (RV-06-001)
1)
2)
Subtract the booking fee throughout.
3)
Divide by the cost per participant.
4)
Least possible n = 7.
5)
Greatest possible n = 35; round the upper bound down.
Ans =
; least 7, greatest 35.