Aphotocopy 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

A) If the page is reduced to 80%, the percent enlargement needed to return it to its original size is; 125%

B) 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 is; 9 times

A) We are told that a page is reduced to 80%.

Let the original size be 100%

Thus;

If we want to return the current size of 80% back to the original size of 100%, then we need to multiply 80% by a rate.

Let this rate be x.

Thus;

80%x = 100%

x = 100%/80%

x = 1.25

Converting 1.25 to percentage gives 125/100 = 125%

B) We want to 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

Since the photocopy machine can reduce copies to 80% of their original size. Then;

First copy;  0.80 × 100% = 80%

Second copy; 0.80 × 80% = 64%

Third copy; 0.80 × 64% = 51.2%

Fourth Copy; 0.80 × 51.2% = 40.96%

Fifth Copy; 0.80 × 40.96% = 32.77%

Sixth Copy; 0.80 × 32.77% = 26.216%

Seventh Copy; 0.80 × 26.216% = 20.97%

Eight Copy; 0.80 × 20.97% = 16.78%

Ninth Copy; 0.80 × 16.78% = 13.42%

Since the ninth copy gives a percentage of less than 15%, then it means the page must be copied 9 times in succession.

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Part a) if a page is reduced to 80%, what percent enlargement is needed to return it to its original size?

Let

x> the percent enlargement

we know that

the original size is the 100%

so

x*80%=100%

x=(100%/80%)

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

therefore

the answer Part a) is

the percent enlargement is 125%

Part 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

we know that

A photocopy machine can reduce copies to 80% of their original size

so

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 Part b) is

the number of times in succession is 9