Questions   
Sort: 
 #3
avatar+33653 
+3
Aug 29, 2020
 #1
avatar+1093 
+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+1093 
+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

2 Online Users

avatar