Alocal dinner theater sells adult tickets for $105 each and children’s tickets for $60 each. for a certain show, the theater sells 84 tickets for a total of $7155. how many of each type of ticket were sold?

write a system of equations that models this problem and then show all the steps to solve your system of equations using the linear combination.

The answer to your question is he sold 47 adult tickets and 37 children tickets.

Step-by-step explanation:

Data

Adult ticket = a = $105

Children ticket = c = $60

Total number of tickets = 84

Total money earn = $7155

Equations

                              a + c      = 84     (I)

                        105a + 60c = 7155 (II)

Multiply equation I by -60

                           -60a  - 60c = -5040

                          105a   + 60c = 7155

Simplify

                          45a               = 2115

                                           a = 2115 / 45

                                           a = 47 tickets

Substitute a in equation I

                          47 + c = 84

                                  c = 84 - 47

                                  c = 37 tickets

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

step-by-step explanation: the answer for wha if rt is 10 centimeters long, and wha is st? it’s 6