Ou have $32 to spend at the music store. each cassette tape costs $5 and each cd costs $9. write a linear inequality that represents this situation. let x represent the number of tapes and y the number of cds.

Let x = # of tapes

Let y = # of cds

Since the amount you spend cannot go over 32 dollars, the amount you buy must be less than or equal to 32 dollars.

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