A bicycle repair shop hires part-time staff alongside 3 full-time staff, each paid \(\pounds 340\) a week. Each part-time worker is paid \(\pounds w\) a wee...
Question 1 Report
A bicycle repair shop hires part-time staff alongside 3 full-time staff, each paid \(\pounds 340\) a week. Each part-time worker is paid \(\pounds w\) a week.
- Write an expression for the shop's total weekly staff cost with \(p\) part-time staff. (1)
- The weekly staff budget is \(\pounds 1500\). With 4 part-time staff hired, form and solve an equation to find \(w\). (3)
- Using this value of \(w\), write a simplified expression for the total weekly cost with \(p\) part-time staff. (2)
- Find the value of \(p\) that gives a total weekly cost of exactly \(\pounds 1980\). (2)
- State, with a reason, whether this value of \(p\) is realistic. (1)
Answer Details
The shop's weekly cost is built from a fixed part (the full-time wages) and a variable part (the part-time wages), so each part of this question either forms that total, substitutes a known value, or solves for an unknown rate.
(a) Three full-time staff at \(\pounds340\) each cost \(3\times340=1020\); adding \(p\) part-time staff at \(\pounds w\) each gives the expression \(1020+pw\). [1 mark]
(b) With \(p=4\), the budget equation is \(1020+4w=1500\). Subtracting 1020 gives \(4w=480\), so \(w=120\); each part-time worker earns \(\pounds120\) a week. [3 marks]
(c) Substituting \(w=120\) into the general expression from part (a) gives the simplified cost formula \(1020+120p\). [2 marks]
(d) Setting this expression equal to \(1980\): \(1020+120p=1980\), so \(120p=960\) and \(p=8\). [2 marks]
(e) Since \(p=8\) is a positive whole number, the shop really could hire exactly 8 part-time staff, so this value is realistic. [1 mark]
This question rewards keeping the formula in terms of \(p\) and \(w\) as long as possible: once \(w\) is pinned down in part (b), every later part is a straightforward substitution rather than a fresh setup.
Download The App On Google Playstore
Everything you need to excel in your exams
