After adding to their wardrobe, the Giant family ordered a new set of furniture that includes four chairs for $2.75 x 10° each. two couches for $1.9 x 101 each and six tables for $7.75 x 10. If they paid with a $5.0 x 10. how much change would they receive?

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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

3 3 6, because in every triangle the longer side is always shorter than the sum of the other two