Two Summer Job Offers
A student is comparing two summer jobs. Job A pays $10.50 per hour for a guaranteed 20 hours per week plus an 8% commission on that week's personal sales; the manager expects staff to put in about 3 additional unpaid hours per week restocking and cleaning. Job B pays $13.75 per hour for 20 hours per week with no commission and no extra hours. Job A's recruiter says average weekly sales run about $1,400, but a slow week can drop to $600. The student can commit to only one job and needs predictable income to cover a $1,200 fall tuition bill over 10 weeks.
1. At what weekly sales volume do the two jobs pay the same gross weekly amount, and which job pays more at $1,400 in sales?
Read the worked answer
Weekly pay models:
- Job A: P = 10.50(20) + 0.08S = 210 + 0.08S
- Job B: P = 13.75(20) = $275
Break-even: 210 + 0.08S = 275 → 0.08S = 65 → S = $812.50 in weekly sales.
At S = $1,400: A pays 210 + 0.08(1400) = 210 + 112 = $322 vs. B's $275 → Job A is ahead by $47/week.
Effective hourly rate for A at $1,400: 322 ÷ 20 = $16.10/hr, compared with B's $13.75/hr.
2. The student needs $1,200 over 10 weeks. Test both jobs under a slow-sales scenario of $600 per week, including Job A's unpaid hours, and recommend a choice.
Read the worked answer
Required weekly pace: 1,200 ÷ 10 = $120/week - both jobs clear this easily, so the real issue is predictability and effective rate.
Slow week, gross: Job A = 210 + 0.08(600) = 210 + 48 = $258; Job B = $275. Job B is ahead by $17.
Including Job A's 3 unpaid hours (23 hours worked):
- Slow week: 258 ÷ 23 = $11.22/hr (below B's $13.75).
- Average week: 322 ÷ 23 = $14.00/hr (only $0.25/hr above B, and only if sales hit $1,400).
Recommendation: Job B. Job A beats Job B only above $812.50 in sales before counting unpaid hours; once the 3 hours are counted, the break-even rises to 210 + 0.08S = 275 × (23/20)... simpler: A's pay per hour worked is (210 + 0.08S) ÷ 23, which equals $13.75 only when S = $1,831.25 - above the recruiter's own average. Job B pays more in a slow week with less variability.
3. The student decides to take Job A anyway. Writing an inequality, what weekly sales figure must be sustained so that 10 weeks of work covers the $1,200 bill even if every week is a slow week?
Read the worked answer
Inequality (10 slow weeks at $600): 10(210 + 0.08S) ≥ 1,200 → 2,100 + 0.8S ≥ 1,200 → 0.8S ≥ −900 → S ≥ −1,125.
Reading the result: the base wage alone yields 210 × 10 = $2,100, which already exceeds $1,200 by $900, so the bill is covered even at $0 in sales. The constraint is not the tuition bill - it is the comparison with Job B.
Reframe to the real question: find S so that Job A at least matches Job B over 10 weeks: 10(210 + 0.08S) ≥ 10(275) → 0.08S ≥ 65 → S ≥ $812.50/week (≈ $8,125 total sales over the summer).
Judgment: the student should commit to Job A only if sales reliably clear $812.50 per week ignoring unpaid hours, or about $1,831 per week once the 3 unpaid hours are valued at Job B's rate. Below that, Job B is the better financial choice despite the lower headline rate.