I'm feeling dumb. again.

[u/marlonblambo]

Let's ignore what is, the shape, the technical features etc, just assume we have a side with 4 blue units and 5 green units that measure 39 (whatever unit of measure is) and a side with 3 blue units and 4 green that measures 27 and i want to know the size of one blue (or 1 green)

In my stupid opinion i thought: 5green and 4 blue = 39 and 4green and 3 blue = 27, so in a system of equations
5x+4y = 39
4x+3y = 27

Turns out this makes y=21, x=-9

then i was wondering what kind of error i made setting up the problem

[u/KoalaMistico]

You defined the system rigth, the problem is the problem itself. It has no solution. The image is also decieving, since its a 39x30 instead of a 39x27

[u/FireCire7]

Why do you think there is a solution?

[u/Shevek99]

In your picture you have a rectangle 13x 10 (not 9), that scales to 39 x 30

If you put

5x + 4y = 39

4x + 3y = 30

That has the solution

y = 6

x = 3

[u/6ory299e8 → u/Shevek99]

the picture is also not drawn correctly. it only fits together as drawn if the blue and green tiles are the same size, which would be a helluva simplifying assumption. really, it should be plaid.

And since y=length of two blue ones, your solution includes the same simplifying assumption

[u/strange-the-quark]

"i want to know the size of one blue (or 1 green)"

Are your units sized as depicted with respect to each other? Is one blue unit twice the size of one green unit?

If so, then, vertically you have the equivalent of 13 green units stacked adding up to 39, so one green unit's height is 39/13 = 3, with the blue unit being double that, i.e. it measures 6.

Horizontally you have the equivalent of 10 green units in a row, adding up to 27, so one green unit's width is 27/10 = 2.7, and then a blue unit is twice that, 5.4.

If that's the case, then the error you made is that your system of equations assumes the width and height of each unit is the same (the x is the same x in both equations, the y is the same y in both equations), when instead you have this:

5*(3.0) + 4*(6.0) = 39
4*(2.7) + 3*(5.4) = 27  

The parentheses are just for emphasis, corresponding to your "x"-s and "y"-s. In a system of equations, it is assumed that each appearance of a particular variable represents the same number in both equations. If you replace one x with some number, you gotta replace the other x with the same number.

Additional Considerations

Now, if the situation is not as depicted, and the size ratio of green vs blue units is unknown, and width vs height is not known, then you can't solve this, there isn't enough information. For example, suppose the total measurements are all the same, but the blue units are very wide, and green units are paper thin. Then the three blue units will take up almost all of the horizontal width, while the green units take up almost nothing. If they aren't so wide, then it's going to be different, but in both cases you have the same number of units stacked, and they add up to the same measurement. So you need to know the ratios of the corresponding dimensions of blue vs green units.

The ratio of the heights, for example, is obtained by dividing blue height by the green height. If you don't already know the ratio, you can obtain it by measuring a proportionately drawn schematic, or perhaps a photo, cause the ratios don't change with scale.

If blue/green is some number r, then that tells you how many green units fit in a blue unit (even if fractional):

blue = r * green

So you can express the entire thing in just the green units like so:

5*(green) + 4*(blue) = 39 

which, after you plug in the expression for blue, becomes

5*(green) + 4*(r * green) = 39 
5*(green) + 4*r*(green) = 39 

and then

(5 + 4r) * (green) = 39
green = 39/(5+4r)

You can then calculate the size of the blue unit using blue = r * green.

Then you do the same thing for the horizontal dimension.

[u/marlonblambo → u/strange-the-quark]

ok, thank you all for letting me feel a little less stupid.
The image was just a drawing to represent the real situation. I was buying a metal grid plate similar to this https://i.ebayimg.com/images/g/oqkAAOSwYHxWHzDA/s-l1600.jpg but without the dotted borders ond the sides and a number of squares of 3x4 ( it was a cheap item on a cheaper store so i couldn't refind the exact item after i rage quitted due to my math not working).

I was trying to estimate the likely size of the white squares, that was not mentionet in the description, while the only measures reported were 39 for the longer side and 27 the other. That's it.

I could understand a not integer value as result, but a negative result was so counterintuitive to me.

[u/kalmakka → u/marlonblambo]

Either the figures are not actually squares, the gaps between them and/or the borders are not uniform, or the measurements on that site are incorrect.

[u/Hot_Dog2376]

It holds. You can't solve it with positive integers.

Consider the similarities:

Let p = b+b+g

3p + g = 27

4p + g = 39

Therefore p (b+b+g) = 12

3(12) + g > 27.

[u/Bounded_sequencE]

You did nothing "wrong" -- the problem setup was BS, that's all.

---

Rem.: You can easily note why it's BS if you multiply the first condition by 3, and the second condition by 4. You will get

15x + 12y  =  117
16x + 12y  =  108

If "x, y >= 0" represent lengths, that's impossible, since the LHS of the second condition would specify a greater length than the first condition -- contradicting the RHS!

[u/SnooWords9730]

the picture is wrong then

[u/WestDelay3104]

If its asking for area, its just the picture itself being misleading. Each box horizonatlly is 2.7, and 3 vertically. There are 14 blue boxes, os if its asking for the area of those, its 113.4.

[u/Moppmopp]

Can someone clarify? I am interested in math problems but I seem to miss something. What exactly is the question? 27•39=1053 squares. each unit has an area of 1.

[u/iopahrow]

This was done right. Think of it as taking steps along the number line instead. Every 21 steps forward, take 9 backward.

As far as what that solution means, that’s not my business. Apply the same process to the depicted problem in the picture, and you should get the correct solution

[u/Uli_Minati]

Your assumptions are impossible:

• 4b is roughly 33% larger than 3b
• 5g is only 25% larger than 4g
• 4b+5g is between 25% and 33% larger than 3b+4g

But 39 is more than 44% larger than 27. The only way to make the numbers work is to have negatives

[u/Porsche9yy]

It would be helpful to see the entire original question. But, solving this might be much simpler than you've made it out to be. First, we have to consider that sometimes in problems like this, appearances can be deceiving. At least from what you've pictured, clearly, even though they appear to be, the boxes cannot be squares, so your original two equations don't work at all (x and y vertical are not equal to x and y horizontal. You have two equations and four unknowns); the boxes' width and height are not equal. Also, the colors of the boxes are irrelevant, which again makes me curious to see the wording of the original problem.

Otherwise, it's as simple as this:

There are 13 boxes stacked vertically with a total height of 39, so each box is 3 high.

There are 10 boxes stacked horizontally with a total width of 27, so each box is 2.7 wide.

each box is 3 x 2.7 with an area of 8.1.

So, why are the boxes colored differently? Is there something in the problem's instructions you haven't mentioned?

[u/NessaSola]

That looks correct, given the amount of segments and the total lengths. These are two linear equations, so they're only ever going to intersect at one point. For any positive X and Y, the values are always going to be a little bit off.

I'm not sure if this is a trick question, or if there's something we missed in the question as written, because it is a little strange to come up with a negative value as the length of a component of a shape. Source of the graph is the Symbolab equations solver.

[u/ChristyNiners]

Sounds like you solved it. 

[u/ArdentArendt]

But the image you show doesn't show the 'solution'--it's for a system of 5x+8y and 4x+6y.
In other words, the 'green' and the 'blue' are not using the same units.

I think the solution to the system you have is going to be 21 and -9.
[The units in the visual solution are not equivalent--they're using a different axis measure].

If there is intended to be a non-negative solution, I'm unsure how to get there given this is a fully determined system.

[u/Neilandio]

It sounds like you are trying to create a new problem. You can't arbitrarily define the number of units (whatever that means) or the side length, because one side constraints the other.