A photocopy machine can reduce copies to 80% of their original size. By copying an already reduced copy, further reductions can

Question

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A photocopy machine can reduce copies to 80% of their original size. By copying an already reduced copy, further reductions can

be made. (a) if a page is reduced to 80%, what percent enlargement is needed to return it to its original size? W incorrect: your answer is incorrect. Seenkey 125 % (b) estimate the number of times in succession that a page must be copied to make the final copy less than 15% of the size of the original. W incorrect: your answer is incorrect. Seenkey 9 time

Mathematics

1 answer:

PIT_PIT [9.1K] · Answer 1 · 2026-03-07T06:00:28+03:00

Part a) When a page is scaled down to 80%, how much enlargement is necessary to bring it back to its original size?

Let

x---------> the percent enlargement

Given the original size is 100%

This means:

x*80%=100%

x=(100%/80%)

x=1.25--------> 1.25=(125/100)=125%

Thus,

The answer to Part a) is

The percent enlargement required is 125%

Part b) Estimate how many successive copies of a page are needed to make the final copy less than 15% of its original size.

Since the photocopy machine reduces sizes to 80% of the original

Therefore:

Copy N 1

0.80*100%=80%

Copy N 2

0.80*80%=64%

Copy N 3

0.80*64%=51.2%

Copy N 4

0.80*51.2%=40.96%

Copy N 5

0.80*40.96%=32.77%

Copy N 6

0.80*32.77%=26.21%

Copy N 7

0.80*26.21%=20.97%

Copy N 8

0.80*20.97%=16.78%

Copy N 9

0.80*16.78%=13.42%-------------> 13.42% < 15%

Therefore,

The answer to Part b) is

The necessary number of copies to achieve this is 9