How can they say math is logical but when applying logic it goes all funky?

Question

I've just spent hours and hours doing maths (in case you couldn't tell by the question). Logic would say that when you have a graph with two lines and you calculate the x and y axis cross points and draw the graph that the point where the two meet would be accurate on the graph after you solved the in-equation of the two lines i.e I drew a graph very carefully, drew in the lines, made sure the scale was ok, but then when I calculated the meeting point it wasn't anything like on my graph. I've spent almost two hours with my boyfriend trying to figure out where I went wrong, he can't find it.. I can't find it.. how come things that work sometimes don't work on others? It's supposed to be math after all ;)

I know my terms aren't correct, that's cos I'm studying math in a foreign language and don't know the English terms :S

1.6x + y < or equal to 120
20x + 50y < or equal to 3000

The point is to find maximum profit.

I got the x and y axis cutting coordinates...
first graph: (0,120)(75,0)
second: (0,60)(150,0)

On my graph I get the meeting point as around (50,40) but after solving the equations (90,24).
Any help would be greatly appreciated :)

Dunno if you need this but...

The maximum profit line goes like 30x + 40y = "biggest profit I can get" and it should cut through the meeting point at -3/4 but the meeting point is supposed to be where the greatest profit is if you get my meaning.. I have a math test tomorrow and this'll come up.. I just know it will lol

Okey dokey.

1. y=120-1.6x
2. y=60-0.4x

The in-equation:
1.6x + y = 120 | *(-50)
20x + 50y = 3000

-80x - 50y = -6000
20x + 50y = 3000

-80x = -6000 | *(-1)
20x = 3000

100x = 9000
x = 9000/100 = 90

20*90 + 50y = 3000
1800 + 50y = 3000
50y = 1200
y = 24

That's fantastic, thank you so much! So basically I shouldn't mess around with the negative numbers so much at just leave them be for a while. You've just aided me in having a good nights sleep, much thanks :)

Answer 1

I get the same intersection point on the graphs... so maybe we need to look at how you solved the two equations.

1.6x + y = 120 | *(-50)
20x + 50y = 3000

-80x - 50y = -6000 | * (-1)
20x + 50y = 3000

80x + 50y = 6000
20x + 50y = 3000

*Subtracting* the equations at this step:
60x = 3000
x = 3000 / 60
x = 50

20*50 + 50y = 3000
1000 + 50y = 3000
50y = 2000
y = 40

-------------------
The graph of the 3 lines are given below:
Pink: 1.6x + y ≤ 120
Green: 20x + 50y ≤ 3000

Red: 30x + 40y ≤ 3100

Answer 2

Give us the two equations and maybe we can work out where you're going wrong.