Gina visited the aquarium with some of her cousins, aunts, and uncles. The group bought 20 admission tickets for $340. Adult tickets cost $20, and children’s tickets cost $15. How many adult tickets and how many children tickets did the group buy? Write a system of equations.

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Step-by-step explanation:

you can't solve x because it is 2 linear equation and you only have one equation

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