00:01
In this question, they say that a photocopy machine can reduce copies to 80 % of their original size.
00:07
By copying an already reduced copy, further reductions can be made.
00:14
In part a, we say, if a page is reduced to 80%, what percent enlargement is needed to return it to its original size? note that on a photocopy machine, the percent enlargement gives the multiple of the new image of the original.
00:34
So, 120 % enlargement means the new image is 20 % larger than the original.
00:44
So it must be enlarged to what percent of its reduced size? so we first, it was reduced to 80%.
00:56
Now what i want to do is i want to convert that into a fraction.
01:01
I want to say 80 % is 80 over 100, which simplifies to 4 fifths.
01:11
And so now, what does the enlargement have to look like? well, for the enlargement, we need the reciprocal of the reduction.
01:20
The reduction was to 4 fifths of the original size, so the enlargement has to be to 5 fourths of the original size.
01:30
Now, 5 fourths is 1 .25 as a decimal.
01:37
And so if i convert that into a percent, i am going to get 125%.
01:43
So, 125 % enlargement, 25 % larger than the reduced size, brings me back to the original size.
01:53
And then in part b, we say, estimate the number of times in succession that a page must be copied to make the final copy less than 40 % of the size of the original.
02:05
So, the idea is, if i reduce once, we reduce to 80 % of the original.
02:15
If i reduce twice, well, i'm going to look at 0 .8 squared...