The Morning Announcements Budget
A school's media club has a budget of $84.00 to print morning-announcement flyers for one month. The print shop charges a flat setup fee of $12.00, then $0.15 per page for the first 200 pages and $0.10 per page for every page beyond 200. The club plans to print the same number of pages each school day. There are 20 school days in the month. The club advisor says, "At $0.15 a page, 20 days of printing should be plenty." A student notes that the budget must also cover a one-time $9.00 poster for the front office, which the advisor forgot to include.
1. Determine the largest whole number of pages the club can print per school day while staying within the $84.00 budget, including the poster. Show your reasoning at each step.
Read the worked answer
Step 1 - Subtract fixed costs. Setup fee $12.00 + poster $9.00 = $21.00. Remaining for pages: $84.00 − $21.00 = $63.00.
Step 2 - Test whether the total stays within the first 200 pages. Printing 200 pages costs 200 × $0.15 = $30.00, which is well under $63.00, so the club will print more than 200 pages total and reach the cheaper rate.
Step 3 - Set up the cost for P total pages (P > 200). Cost = $30.00 (first 200 pages) + $0.10 × (P − 200). Set this ≤ $63.00: $30.00 + $0.10(P − 200) ≤ $63.00 → $0.10(P − 200) ≤ $33.00 → P − 200 ≤ 330 → P ≤ 530.
Step 4 - Convert to pages per day. 530 ÷ 20 = 26.5, so the largest whole number per day is 26 pages (26 × 20 = 520 total pages).
Check: 520 pages → $30.00 + $0.10(320) = $30.00 + $32.00 = $62.00; plus $21.00 fixed = $83.00 ≤ $84.00. Going to 27/day (540 pages) gives $30.00 + $34.00 + $21.00 = $85.00, over budget. Answer: 26 pages per day.
2. The advisor's statement assumes $0.15 per page applies to all pages. Explain in 2–3 sentences why this assumption changes the answer, and identify which cost the advisor overlooked.
Read the worked answer
The $0.15 rate applies only to the first 200 pages; beyond that the rate drops to $0.10, so a flat $0.15-per-page model overestimates the cost of large print runs and would make the club think it can afford fewer pages than it actually can. The advisor also overlooked the one-time $9.00 poster, which reduces the money available for printing. These two errors push in opposite directions, which is why the estimate must be rebuilt from the tiered structure rather than a single rate.