A clothing business finds there is a linear relationship between the number of shirts, n ,it can sell and the price, p , it can charge per shirt. In particular, historical data shows that 7000 shirts can be sold at a price of $ 79 , while 22000 shirts can be sold at a price of $ 4 . Give a linear equation in the form p = m n + b that gives the price p they can charge for n shirts. Show your work.

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Step-by-step explanation:

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step-by-step explanation:

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