A simple one..but I cant figure it out!

[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?

 

[galactus]

No, not quite.

Think about it. For simplicity, let's use the number 1.

1+.5(1)=1.5
1.5+.5(1.5)=2.25
2.25+.5(2.25)=3.375
3.375+.5(3.375)=5.0625

There is 4-50% enlargements. How much larger is 5.0625 than 1?.

 

[stapel]

FYI: Similar example.

 

[galactus]

Sorry Stapel, I had not seen that post. Purely coincidental.

 

[soroban]

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: $\displaystyle 1.5\,\times\,3.375X \;=\;5.0625\,\approx\,5.1$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

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 $\displaystyle 40$
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.