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?

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:



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.

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since the cosine is the ratio of the adjacent side to the hypotenuse, you can see that cos 60° = ½. answer. according to the property of cofunctions (topic 3), sin 30° is equal to cos 60°. sin 30° = ½.