SOLUTION: Javier works in a photo lab and needs to make a reduced copy of a photograph that is 8 inches long. The customer wants the copy to have a length of 4.5 inches. Each time he presses

Question 1019315: Javier works in a photo lab and needs to make a reduced copy of a photograph that is 8 inches long. The customer wants the copy to have a length of 4.5 inches. Each time he presses the reduce button on the copier, the copy is reduced by 12%. Javier and his boss had an argument, because Javier claimed that pressing the button 5 times would be enough to fulfill the customer's request. His boss said that pressing the button 5 times would result in a length less than the desired 4.5 inches. Which of the following conclusions can be made?
Javier is correct and he should press the button five times
Javier's boss is correct and he should press the button five times.
Javier is correct and he should not press the button five times.
Javier's boss is correct and he should not press the button five times.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe the selection needs to be:

javier's boss is correct and he should not press the button five time.

pressing the button any number of times will not result in a reduction from 8 inches to 4.5 inches.

here's what happens with every press of the button.

start at 8 inches.
press once, then you get 8 - .12 * 8 = 7.04 inches.
press once again, then you get 7.04 - .12 * 7.04 = 6.1952 inches.
press once again, then you get 6.1952 - .12 * 6.1952 = 5.451776 inches.
press once again, then you get 5.451776 - .12 * 5.451776 = 4.79756288 inches.
press once again, then you get 4.79756288 - .12 * 4.79756288 = 4.221855334 inches.

pressing 4 or 5 times gets close but does not get 4.5 inches exactly.

the true answer is somewhere in between.

he should use custom reduction and reduce the original to 4.5/8 = .5625 * the original length.

.5625 * 8 = 4.5 inches.

he might be able to use custom length, in which case he would specify the length to be 4.5 inches and the copier would handle the rest.

if he needs to reduce it by a certain percent, then he needs to reduce 8 by .4375 * 8 which would result in 8 minus 3.5 which give him a length of 4.5 inches.

there are various ways it can be done, depending on the capabilities of the copier.

the bottom line is, however, that javier's boss is correct and he should not press the button five times.

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