A digital photography archive consists of RAW files and JPEG files. Initially, the RAW fil… — SAT

A digital photography archive consists of RAW files and JPEG files. Initially, the RAW files account for $80\%$ of the total storage space used by the archive. To reduce the storage space, the photographer compresses $40\%$ of the RAW files into JPEGs, which reduces the storage space of those specific files by $62.5\%$ . If the remaining uncompressed RAW files now account for $x\%$ of the updated total storage space of the archive, what is the value of $x$ ?

Answer: 60

Answer

The remaining uncompressed RAW files occupy 48% of the initial total storage space, and the updated total storage space is 80% of the initial storage space. The percentage of the updated total storage space occupied by the uncompressed RAW files is therefore 60%.

The remaining uncompressed RAW files occupy

48\%

of the initial total storage space, and the updated total storage space is

80\%

of the initial storage space. The percentage of the updated total storage space occupied by the uncompressed RAW files is therefore 60%.

Step-by-Step Solution

Define variables for initial storage space.

Initial RAW space is

0.80T

; initial JPEG space is

0.20T

Establishes the baseline values relative to the initial total storage space

T

Calculate the space occupied by the portion of RAW files to be compressed and the remaining uncompressed RAW files.

Compressed RAW space is

0.32T

; remaining uncompressed RAW space is

0.48T

Splits the RAW files into the group that changes size and the group that remains unchanged.

Determine the new space occupied by the compressed files after the

62.5\%

reduction.

Reduction is

0.20T

; new space of compressed files is

0.12T

Calculates the impact of the compression percent change on the target subpopulation.

Calculate the updated total storage space of the archive.

Updated total storage space is

0.80T

Summing all updated file spaces (

0.48T

uncompressed RAW +

0.20T

original JPEG +

0.12T

newly compressed files) provides the new base for the final percentage calculation.

Compute the final percentage of the updated total storage space occupied by the uncompressed RAW files.

x = 60

Dividing the remaining uncompressed RAW space (

0.48T

) by the new total space (

0.80T

) gives the updated percentage.

Key Concept

Multi-step percent change and relative base calculations.

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