Question

Mr. Nicolas is putting up strings of blue and white lights for the holidays. The ratio of blue to white lights is 5 to 6. If he has 77 strings, how many strings are white lights?

Answer 1

There are 42 strings of white lights.

Let x be the number of blue lights.  Then 77-x is the number of white lights.  We can set up a proportion:

$\frac{5}{6}=\frac{x}{77-x}$

Cross multiplying we have:
5(77-x) = 6*x
385-5x = 6x

Gathering all of the variables on the right side, we add 5x:
385-5x+5x = 6x+5x
385 = 11x

Divide both sides by 11:
385/11 = 11x/11
35 = x

There are 35 blue lights.  This means there are 77-35 = 42 white lights.