Marni dance in a contest to raise money for an animal shelter marni raise 30+ $1.80 per minute that she danced she raised a total of $264 let x equal the number of minutes marni danced what expression completes the equation to determine the total amount of minutes marni danced how many minutes did marni dance

264 = 30 + 1.80x

234 = 1.80x

130 = x

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