Hello, Jamie27!
A duplicating machine enlarges a picture 50%.
If that enlarger is used 4 times, about how many times as large as the original picture will the final picture be?
A) 2
B) 5
C) 6
D) 5.1
I believe the answer to be A because if it is enlarged 50% each time to make 4 times it would equal 2 right? \(\displaystyle \;\) no
Every enlargement increases the area of the picture by 50%.
The new picture is 150% of the previous area
. . . that is, \(\displaystyle 1.5\) times the previous area.
If \(\displaystyle X\) is the orignal area, the first enlargement has an area of: \(\displaystyle 1.5X\)
The second enlargement has an area of: \(\displaystyle 1.5\,\time\,1.5X \:= \:2.25X\)
The third enlargement has an area of: \(\displaystyle 1.5\,\times\,2.25X \:=\:3.375X\)
The fourth enlargement has an area of: \(\displaystyle 1.5\,\times\,3.375X \;=\;5.0625\,\approx\,5.1\)
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You fell into a famous 'trap" . . . combining percents (often quite dangerous).
Your base pay is $1000.
Your boss promises you two consecutive 20% raises.
He figures 20% + 20% = 40%
\(\displaystyle \;\;\)then \(\displaystyle 40%\,\times\,1000\:=\:400\)
and give you your new paycheck: $1400 \(\displaystyle \;\)
. . . wrong!
The first raise: \(\displaystyle 20\%\,\times\,1000\:=\:200\), increases your salary to $1200.
The second raise: \(\displaystyle 20\%\,\times\,1200\:=\:240\), increases your salary to $1440
Here's another "trap" . . .
Your boss asks you to take a 10% cut in salary during some rough times.
He promises to give you a 10% raise after recovering from the slump.
Fair enough?
The 10% cut means: \(\displaystyle 10\%\,\times\,1000 \;=\:100.\;\) Your reduced salary is $900.
Then you get a 10% raise: \(\displaystyle 10\%\,\times\,900 = 90.\:\)Your new salary is $990
\(\displaystyle \;\;\)You are
not back to your original salary . . . you've lost $10.
