Jake’s computer has two hard drives that can store the same amount of data. One drive is 3 full while the other is 2 full. 85 a What fraction of the total amount of storage space is empty? b Each hard drive can store 750 gigabytes of data. Jake wants to download 150 gigabytes of data. Does he have enough space? Explain your answer.
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Given:
1st drive is 3 full ⇒ Storage space filled = 1/3
2nd drive is 2 full ⇒ Storage space filled = 1/2
The capacity of each drive = 750 GB
The amount of data Jake wants to download = 150 GB
To Find:
a. What fraction of the total amount of storage space is empty?
b. Does Jake have enough space to download the data?
Calculation:
(a) Let the storage space of each drive be x
⇒ Total space = 2x
⇒ Space filled on 1st drive = x/3
& Space filled on 2nd drive = x/2
⇒ Empty space on 1st drive = x - x/3 = 2x/3
& Empty space on 1st drive = x - x/2 = x/2
- Total empty space = 2x/3 + x/2 = 7x/6
- The fraction of empty space = (7x/6)/2x
⇒ The fraction of empty space = 7/12
(b) The storage of one drive = 750 GB
⇒ The total storage of both drives = 1500 GB
- The total free space = 7/12 of 1500 = 875 GB
- Since the free space on disks is 875 GB, hence Jake can easily download 150 GB of data.
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