The parking lot has spaces for 450 cars. The ratio of spaces for full sized cars to compact cars is 11 to 4.
Write a system of equations to solve the problem. How many spaces are for full sized cars? how many spaces are for compact cars?

Question

The parking lot has spaces for 450 cars. The ratio of spaces for full sized cars to compact cars is 11 to 4. 
Write a system of equations to solve the problem. How many spaces are for full sized cars? how many spaces are for compact cars?

anonymous · Answer

F + C = 450     F/C = 11/4

ny,ny · Answer

ok, yeah I had those equations down too. 

f + c = 450
f=450-c 
---------------
f/c = 11/4
450 - c/ c = 11/4
450 = 2c x 11/4

am i going the right way?

ny,ny · Answer

i feel like im doing something wrong...

anonymous · Answer

You were doing ok up until that last equation.  It might be because you did not put 450 - c in parentheses because both those terms are over c, so 450 - c = (11c)/4    Then,   450 = (15c)/4       1800 = 15c     c = 120    so f=330

ny,ny · Answer

how did 11c become 15c?

anonymous · Answer

I added c to each side in the form of 4c/4 because the right side had a 4 in the denominator.

ny,ny · Answer

ok. could you explain that out a little better please? I'm kind of confused.

ny,ny · Answer

sorry about that.

anonymous · Answer

$$450 - c = \frac{ 11c }{ 4 }$$so$$450 = \frac{ 11c }{ 4 } + c$$so$$450 = \frac{ 11c }{ 4 } + \frac{ 4c }{ 4 }$$

ny,ny · Answer

oh ok. that helps a lot better. thank you.

anonymous · Answer

you're welcome!