There are 42 students in a school lunch , 25 eat rice, 15 eat spaghetti and 11 eat neither rice nor spaghetti. (a) Draw a venn diagram to illustrate this information. (b) How many students eat both rice and spaghetti? (c) How many students eat at most one of the two types of food?

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

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step-by-step explanation:

equals the constant of proportionality.

solve for