Question

kevin is converting his grandfather’s cd collection into music files on his computer. the collection contains 48 cds. each cd is an average of 39 minutes and 51 seconds long. the size of each music file is about 0.91 megabytes per minute. which number is the best estimate of the total space, in megabytes, that will be used by these music files?
a 1,800
b 9,000
c 180,000
d 9,000,000

Explanation:

Step1: Convert seconds to minutes

51 seconds is approximately 51/60 = 0.85 minutes. So each CD's length is about 39 + 0.85 ≈ 40 minutes (rounding for estimation).

Step2: Calculate space per CD

Each minute is about 0.91 megabytes, so per CD: 40 0.91 ≈ 40 0.9 = 36 megabytes (estimating 0.91 as 0.9 for simplicity).

Step3: Calculate total space for 48 CDs

48 CDs 36 megabytes/CD. Estimate 48 as 50, so 50 36 = 1800? Wait, no, wait. Wait, 4836: 4830=1440, 486=288, total 1728. But wait, maybe my initial minute conversion was wrong. Wait, original time: 39 minutes and 51 seconds. 51 seconds is 51/60 = 0.85, so 39.85 minutes, approx 40 minutes. Then per CD: 40 0.91 ≈ 36.4 megabytes. Then 48 CDs: 48 36.4. Let's estimate 48 as 50, 36.4 as 36: 5036=1800? But wait, the options are a)1800, b)9000, c)180000, d)9000000. Wait, maybe I misread the number of CDs. Wait, the problem says "the collection contains 48 CDs". Wait, maybe my calculation is wrong. Wait, 0.91 megabytes per minute. Each CD is 39 minutes 51 seconds, so ~40 minutes. So per CD: 40 0.91 ≈ 36.4 MB. Then 48 CDs: 48 36.4. Let's calculate 4836.4: 4830=1440, 486.4=307.2, total 1747.2, approx 1800. But wait, maybe the number of CDs is 480? No, the problem says 48. Wait, maybe I made a mistake in the time. Wait, 39 minutes and 51 seconds is 39.85 minutes, so ~40. Then 400.91=36.4. 4836.4≈1747, which is close to 1800 (option a). But wait, maybe the question is about 480 CDs? No, the problem says 48. Wait, maybe the 0.91 is per second? No, the problem says "0.91 megabytes per minute". Wait, let's recheck: "the size of each music file is about 0.91 megabytes per minute". So per minute, 0.91 MB. So each CD is 39 min 51 sec ≈40 min. So per CD: 40 0.91 ≈36.4 MB. 48 CDs: 48 * 36.4 ≈1747, which is ~1800 (option a). But wait, the options have 1800, 9000, etc. Maybe I misread the number of CDs. Wait, maybe it's 480 CDs? No, the problem says 48. Wait, maybe the time is 39 minutes and 51 seconds per track, but no, per CD. Wait, maybe the question is in the translation. Wait, let's do exact calculation:

Total minutes per CD: 39 + 51/60 = 39.85 minutes.

Space per CD: 39.85 0.91 ≈ 39.85 0.9 = 35.865, plus 39.85 * 0.01 = 0.3985, total ≈36.2635 MB per CD.

Total CDs: 48.

Total space: 48 36.2635 ≈ 48 36 = 1728, 48 * 0.2635 ≈12.648, total ≈1740.648, which is approximately 1800 (option a). But wait, the options have 1800, 9000, 180000, 9000000. So 1800 is option a. But maybe I made a mistake in the number of CDs. Wait, maybe it's 480 CDs? No, the problem says 48. Wait, maybe the 0.91 is per second? No, the problem says "per minute". So I think the correct estimate is 1800, option a.

Answer:

a. 1,800