Jason received a $50 gift certificate for his birthday. he wants to buy a dvd and a poster from a media store. (assume that sales tax is included in the prices.) write and solve a linear inequality to show how much he would have left to spend after making these purchases. all dvd's only $14.95 all cd's only $11.25 all posters only $10.99

In the given question , it is given that Jason received a $50 gift certificate for his birthday. He wants to buy a DVD and a poster from a media store.

Let the amount left after doing these purchases be $x .

And the total must be less then or equal to 50, that is

And that's the required inequality.

Subtracting 25.94 from both sides

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