Tasty Italian’s lunch special repeats every 6 days. Delicious Meatballs’ lunch special repeats every 8 days. Both restaurants are serving spaghetti as their lunch specials today. What is the earliest number of days both restaurants serve spaghetti as their lunch specials again?

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c - they will have the same distribution

step-by-step explanation:

this is the only one that could make sense. : )

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