Let's start by calculating the cost of the first 10 boxes, which totals $75, and the next 10 boxes cost $55.
Together, these 20 boxes amount to $130 spent. With $18 remaining, you can purchase 4 more boxes since 18 divided by 4.5 equals 4.
Therefore, the maximum number of boxes you can buy with $148 is 24.
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
Calculating gives us 73 - 27 = 46
Next, 46 / 100 × 2628 = 1208
Adding together gives 2628 + 1208 = 3836
