Agym charges $50 dollars per month after an initial membership fee. a member has paid a total of $320 after 6 months. write an equation that gives the total cost of gym membership as a function of the length of membership (in months).

x6+50=320

x6=50-50=320-50

x6=270

x6/6=270/6

x=45

So this person is spending $45 a month.

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

beth buys 10 x shirts and still has more than 100 in her account