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# the amount of the price

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if the price of a pencil is 36% lower than the price of a pen,then the price of a pen is ?

1.)36%higher than a pencil

2.)43.75 higher than a pencil

3.)56.25 % higher than a pencil

4.)64% higher than a pencil

Guest Feb 17, 2015

#1
+89889
+10

If the price of a pencil is 36% lower than the price of a pen, then the pencil's price is 1- 36% of the pen's price =.64pen

For argument's sake, let the pen's price be 1  .....Then the pencil's price = .64

Then

.64( 1 + P) = 1     where P is the % we're looking for...divide both sides by .64

1 + P = 1/.64

1 + P =  1.5625     subtract 1 from both sides

P = .5625  =  56.25%

Then the pen is 56.25% more than the pencil.

Another way to see this is that .36 must be added to the pencil's price of .64 to get the pen's price.

Thus 36/64 = 56.25% of the pencil's price must be added.......

.

CPhill  Feb 17, 2015
#1
+89889
+10

If the price of a pencil is 36% lower than the price of a pen, then the pencil's price is 1- 36% of the pen's price =.64pen

For argument's sake, let the pen's price be 1  .....Then the pencil's price = .64

Then

.64( 1 + P) = 1     where P is the % we're looking for...divide both sides by .64

1 + P = 1/.64

1 + P =  1.5625     subtract 1 from both sides

P = .5625  =  56.25%

Then the pen is 56.25% more than the pencil.

Another way to see this is that .36 must be added to the pencil's price of .64 to get the pen's price.

Thus 36/64 = 56.25% of the pencil's price must be added.......

.

CPhill  Feb 17, 2015
#2
+93654
+5

Thanks Chris this is a good question.  I am just going to think about it myself for a bit.

My pencil is a lead pencil so L for the pencil

and my pen is Blue so B for the pen

$$\\64\%\; of\; B=L\\ 0.64B=L\\ divide both sides by 0.64\\ B=\frac{L}{0.64}=\frac{1}{0.64}\times L = 1.5625L$$

So the blue pen is 156.25% the cost of the lead pencil

In other words the blue pen is 56.25% more expensive than the lead pencil.

Melody  Feb 17, 2015
#3
+89889
+5

It DOES seem a bit tricky, at first......I had to think for a few minutes about how to set it up...LOL!!!!

CPhill  Feb 17, 2015
#4
+93654
+5

It is horrible when the obvious letter to use eg P for pencil and P for pen does not work (because they are the same)  If you can swap them for some other letters that still makes sense, like I did, then it gives you one less thing to get really confused about.

Melody  Feb 17, 2015