AlgebraVery hardSolve equal-cost equation then compute requested total
Algebra practice question
A documentary film crew is choosing between two equipment rental plans for a shoot lasting a whole number of days. Plan A charges a one-time insurance fee of $1,500 plus $255 for each shooting day. Plan B charges a one-time fee of $3,000 plus $195 for each shooting day plus an additional $30 for each shooting day for an on-site technician. For the length of this crew's shoot, the two plans produce exactly the same total cost.
What is that total cost?
- A. $7,875
- B. $12,750
- C. $14,250Correct
- D. $39,750
Answer: C. $14,250
Let d be the number of shooting days. Plan A costs 1500 + 255d and Plan B costs 3000 + 195d + 30d = 3000 + 225d. Setting them equal: 1500 + 255d = 3000 + 225d, so 30d = 1500 and d = 50. The total cost is 1500 + 255(50) = 1500 + 12,750 = $14,250 (check Plan B: 3000 + 225(50) = $14,250). (A) $7,875 comes from omitting the technician's $30 per day, giving 60d = 1500, d = 25, and 1500 + 255(25). (B) $12,750 comes from finding d = 50 correctly but reporting only the daily charges, forgetting the $1,500 one-time fee. (D) $39,750 comes from adding the two one-time fees instead of subtracting them, giving 30d = 4500 and d = 150.
Why the other answers are wrong
- A. $7,875
- You left out Plan B's $30-per-day technician, which made Plan B $195/day and gave d = 25. Including the technician makes Plan B $225 per day, so d = 50.
- B. $12,750
- You found d = 50 correctly, but $12,750 is only the 255 × 50 daily charge — add Plan A's $1,500 one-time insurance fee to get the total cost.
- D. $39,750
- You added the one-time fees ($1,500 + $3,000) instead of subtracting to compare them; the equation 1500 + 255d = 3000 + 225d gives 30d = 1500, so d = 50, not 150.
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