The school that Anthony goes to is selling tickets for a choir concert. On the first day of ticket sales his school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. What is the price of a senior citizen ticket?

A senior citizen costs $8

Step-by-step explanation:

Represent senior citizens with S and children with C.

The first day is represented as:

The second day is represented as:

Required

Solve for C and S

Make C the subject in the first equation

Substitute 38 - 3S for C in the second equation

Collect Like Terms

Divide through by -3

Recall that:

Hence, a senior citizen costs $8

nlgqer

step-by-step

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