T. L Hanna High School’s theatre department is putting on their annual play. Tickets (t) are $12 each. Parking is $5 flat. You and your family attend the play and pay a total of $53. How many tickets did your family purchase?

No. of ticket bought is 4

Step-by-step explanation:

Let the no. of ticket bought be x

Given cost of 1 ticket = $12

Therefore cost x ticket = x*cost of 1 ticket = x*$12 = $12x

parking fee = $5

given that it is flat so, whatever be the no. of ticket bought or family member,

the parking cost will remain $5 only.

Total money paid by family  = parking charge + cost x ticket = 5+12x

But , given that family paid total of $53

then

5 + 12x = 53

=> 12x = 53-5 = 48

=> x = 48/12 = 4

Thus, no. of ticket bought is 4.

This can be validated as  shown below

cost of 4 ticket as 12 each will be = 12*4 = 48

thus total money paid = $(48+5 )= $53

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