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ilorty

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Usernameilorty
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 #1
avatar+1094 
+3

I wonder why that person has the time to see how much the totals cost, when he/she could have just checked the price...indecision

 

Whatever the case, we need to help the person out, because they could not bother to go and check the unit price, and decided to create a math problem for it.

 

To start, let's label each item with a variable. 
 

Notebook = n

Binder = b

Pencil = p

 

With these variables set, we can create some equations!

 

3n + 2b + p = 6

2n + b + 2p = 6.92

n + 3b + 3p = 10.84


We see that here are 3 variables, which means this is a 3 variable system of equations .

 

Add the two top equations:

 

5n + 3b + 3p = 12.92

 

Subtract bottom equation:

 

4n = 2.08

n = 0.52

 

Now that we know how much a notebook costs, we can plug that value back into the equations:

 

3(0.52) = 1.56

2(0.52) = 1.04

1(0.52) = 0.52

 

So:

 

1.56 + 2b + p = 6

2b + p = 4.44

1.04 + b + 2p = 6.92

b + 2p = 5.88

0.52 + 3b + 3p = 10.84

3b + 3p = 10.32

 

We now know that:

 

p = 4.44 - 2b

 

So:

b + 2(4.44 - 2b) = 5.88

b + 8.88 - 4b = 5.88

-3b = -3

b = 1

 

Therefore, à binder costs one dollar.

 

Also, it would be nice if you actually read my answer from start to end, because it took me 27 minutes to compose it.

 

:)

 


 

Aug 29, 2020
 #1
avatar+1094 
+2


 

That is the image but smaller, so no one has to scroll a hundred times just to read the problem. Anyways, there are two methods to solve this problem.

 

METHOD 1: 
 

To begin, we first find the "unit-rate".      <------ a real link

 

For Trevon, that is 01/10 per hour. For Cody, that is 1/7 per hour. 
 

Together, they paint 17/70 of the attic in one hour. The time they spent with the whole attic is just the reciprocal, which is 70/17. Sadly, this does not come out well, but you could just say 4 hours and 2/17 of an hour (Rounded to 4 hours and 7 minutes). Does not make sense, but that's the fault of the creator of the problem, as they should have known that this is not possible. (Or my fault for doing it wrong)

 

METHOD 2: 

 

Using the formula:

 

ab/a + b = 7(10)/7 + 10 = 70/17, same as before, 4 hours and 2/17 of an hour. (Rounded to 4 hours and 7 minutes)

 

:)

Aug 29, 2020
 #1
avatar+1094 
+2

Well, you will eventually finish the pizza....after infinite years. It's probably moldy by then, so not a good way to eat pizza. I wonder what this guy is doing with his/her life to eat HALF A PIZZA in one sitting, add later eating on fourth. Just eat the whole pizza directly! Then there would not have to be any math problem, OR moldy pizza. 

 

All things aside, it is a word problem, and most of the time, they are pretty unrealistic. 

 

For the problem:

Sure, we COULD just keep on figuring out each half of the pizza, and yadda yadda yadda, but there is an easier way. But before we get into the easier way, let's go through the hard way, just to justify the easy way. 

 

HARD WAY:

 

Description: This is the way for people with a lot of time, just like the guy who keeps on eating half his pizza instead of the whole.

 

Idea:

 

Start: 1 whole

Half 1: 1/2

Half 2: 1/4

Half 3: 1/8

Half 4: 1/16

Half 5: 1/32

 

Conclusion: That dude must have a lot of time up his sleeve to be forever eating pizza and solving math problems the hard way.

 

EASY WAY:

 

Desription: For people who like exponents. If you are allergic to them, then do it the hard way. We won't judge. (Unless you are that dude who keeps on eating half his pizza)

 

Idea:

 

Simply put, this question is just asking for 2^-5, which is basically halfing as you go. This is:

 

1/2^5 = 1/32

 

Conclusion: We now know that whoever tried this method is immune to exponents, yet still like to eat moldy pizza.

 

:)

Aug 28, 2020
 #1
avatar+1094 
+1

Assuming you know what the binomial theorem is...(tap the link, if you dont know, and go to the section that says "statement")

 

We could just use the binomial theorem to expand right away, but that would be not so smart, as the number "8" is considered small enough to be calculated with this picture:

 

 

 

We can see already factored out coefficients on the 9th row! Isn't that just awesome...?

 

All that being said, we can start! 

 

If we just used (x + y)^8 to start, we see that this expands out to: 

 

 

using the binomial theorem and the triangle, formally known as "Pascal's Triangle".

 

But, instead of y, we have -2y... so what do we do? Simple: we just plug that in for y! This will become:

 

 

There! An answer that you can't just copy and paste, isn't that awesome??? Anyways, here is a 3D graph for geeks:

 

 

 

:)

 

 

Citations: All images generated with WolframAlpha graphing

Aug 28, 2020