Question

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 1

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

Answer 2

Javier's boss is correct and he should not press the button five times.

Explanation:

The given scenario says that Javier claimed that pressing the button 5 times would be enough to fulfill the customer's request.

We shall check the claim.

We will start at 8 inches.

Press once,
`8-0.12*8=7.04` inches.

Pressing again, we get
`7.04-.12*7.04=6.1952` inches.

Again we get
`6.1952-.12*6.1952 = 5.451776` inches.

Again we get
`5.451776-.12*5.451776 =4.79756288` inches.

Again we get
`4.79756288-.12*4.79756288= 4.221855334` inches.

We can clearly see here, that pressing 4 or 5 times does not get 4.5 inches exactly as claimed by Javier.

Therefore, Javier's boss is correct and he should not press the button five times.