Question

Hello I need help with this
A photographer increases the size of a picture by 50%. The image still was not large enough so she increased the image by another 25%. What percent of its original size is the picture now?

Answer 1

By increasing a value \(x\) by \(p\) percent, we are doing:
\[
x(1+p)=x'
\]Where \(x'\) is our new value.

Using this, how would you find the final value after resizing twice?

Answer 2

I am lost

Answer 3

I am not sure if this is correct or not, but I believe that we have to do:
x(50%+25%). That would equal to the percentage of the resizing after done with 25%.

Answer 4

But what is x?

Answer 5

'x' is the original size of the picture before the resizing.

Answer 6

Would the equation %change= change /100*100 work?

Answer 7

It can if you are changing the percent to a decimal.

Answer 8

Well it didn't work after all.

Answer 9

The answer was incorrect?

Answer 10

Yes I used 75 % as the percent change and the correct answer should have been 187.5 and I have no idea why

Answer 11

No, it's incorrect.
You have to use:
\[
x(1+p)=x'
\]So, then you would have:
\[
x(1+.5)=x'
\]And, then, we wish to increase it again, so:
\[
x(1+.5)(1+.25)=\underbrace{x(1.875)}=(1+.25)x'=x''
\]Which is our final answer.

Answer 12

What is this formula called

Answer 13

And why are you adding 1 to the percentages

Answer 14

Because we wish to *expand* the figure by 50%, say. Hence, we want to add 50% of the size to the original figure. That means that, for our original size \(s\), we wish:
\[
s+.5s=(1+.5)s
\]

There is no name for the formula; it also doesn't help to know names---understand it intuitively, instead.

Answer 15

But I don't know what s is?

Answer 16

Wait can s be 100?

Answer 17

Shall i help if i may?

Answer 18

I would try

Answer 19

Let the origanal size of the image be x Ok?

Answer 20

Yes

Answer 21

''A photographer increases the size of a picture by 50%. ''

SO