In a recent air quality study, there were 64 unhealthy air quality days in city a. this is 4 more than twice the number of unhealthy air quality days in city b. how many unhealthy air quality days were there in city b?

The answer to your question is: 30 days

Step-by-step explanation:

City A has 64 unhealthy air quality days this is 4 more than twice the number of unhealthy air quality days in City B.

# unhealthy days in city A = 64

# unhealthy days in city B = B

Equation

                          64 = 2B + 4

                          64 -4 = 2B

                          60 = 2B

                          B = 30 days

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4