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Bunuel
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{x} denotes the smallest integer greater than or equal to x. 06 Jun 2026, 05:30
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\(\{x\}\) denotes the smallest integer greater than or equal to \(x\). A video editing firm charges $140 for editing the first 15 minutes of a film or films up to 15 minutes in length. It then charges $20 for editing each additional 15 minutes of film or length of film up to 15 minutes. Which of the following would represent the charge in dollars for editing a film that has a length of \(p\) hours?

(A) \(120 + 20\{4p\}\)

(B) \(120 + 20 \{p\}\)

(C) \(140 + 80 \{p\}\)

(D) \(140 + 20\{4p\}\)

(E) \(160 + 20\{4p\}\)
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{x} denotes the smallest integer greater than or equal to x. 08 Jun 2026, 05:15
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Bunuel
\(\{x\}\) denotes the smallest integer greater than or equal to \(x\). A video editing firm charges $140 for editing the first 15 minutes of a film or films up to 15 minutes in length. It then charges $20 for editing each additional 15 minutes of film or length of film up to 15 minutes. Which of the following would represent the charge in dollars for editing a film that has a length of \(p\) hours?

(A) \(120 + 20{4p}\)

(B) \(120 + 20{p}\)

(C) \(140 + 80{p}\)

(D) \(140 + 20{4p}\)

(E) \(160 + 20{4p}\)
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{x} denotes the smallest integer greater than or equal to x. 10 Jun 2026, 03:20
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There must be some algebraic approach, sure, but I simply took p=1.

On doing that, the total cost comes out to be 140+20+20+20=200.

Only option A comes out to be 200. Hence, it is the answer. I would be happy to understand the algebraic solution too.
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{x} denotes the smallest integer greater than or equal to x. 11 Jun 2026, 04:00
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how did you get the 20+20+20?

shashag
There must be some algebraic approach, sure, but I simply took p=1.

On doing that, the total cost comes out to be 140+20+20+20=200.

Only option A comes out to be 200. Hence, it is the answer. I would be happy to understand the algebraic solution too.
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{x} denotes the smallest integer greater than or equal to x. 11 Jun 2026, 05:28
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We assume p to be 1 hour. An hour has 4 parts of 15 minutes. The first 15 minutes are 140. The remaining 3 parts of 15 minutes are priced at 20 each. Hence, 140+20+20+20.

I hope it's clear.
PurvaG
how did you get the 20+20+20?


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{x} denotes the smallest integer greater than or equal to x. 11 Jun 2026, 07:22
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Hi PurvaG,

shashag picked p = 1 hour just to test the answers with a concrete number, so let's see where those three $20s come from.

The firm bills film in 15-minute blocks:
- The first15 minutes cost $140.
- Every15-minute block after that costs $20.

Now take 1 hour. One hour = 60 minutes, and 60 ÷ 15 = 4 blocks of 15 minutes each. Line them up:

- Block 1 (0-15 min) - $140 (this is the first-block price)
- Block 2 (15-30 min) - $20
- Block 3 (30-45 min) - $20
- Block 4 (45-60 min) - $20

So after the first block, 3 blocks are left, and each adds $20. That's the 20 + 20 + 20. Total = 140 + 60 = $200.

The key idea: the $140 already pays for the first block, so you only charge $20 for the remaining blocks - here, 4 total minus 1 = 3 of them.

Quick check to lock it in: try p = 0.5 hour (30 minutes).
- 30 ÷ 15 = 2 blocks.
- First block = $140, then just 1 leftover block = $20.
- Total = $160.

Notice you always have (number of blocks - 1) of the $20 charges. In algebra, the blocks are {4p}, the leftovers are {4p} - 1, and the cost is 140 + 20({4p} - 1) = 120 + 20{4p} - which is exactly choice A.

Answer: A

PurvaG
how did you get the 20+20+20?


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