Question

One hundred and twenty people attended a musical. The total amount of money collected for tickets was $1515. Prices were $15 for regular adult admission, $12 for children and $10 for senior citizens. Twice as many children's tickets as regular adult tickets were sold. Write a system of equations to find the number of children, adults, and senior citizens that attended the musical. Then solve the system by using a matrix equation and the inverse matrix.

Answer 1

 Hope this will help.

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Answer 2

Answer:

70 children, 35 adults, 15 seniors

make me brainly

Step-by-step explanation:

if we label variables a for # of adult, c for # of children, and b for # of senior citizen.  

we can now come up with a system of equations from the information given.  

people attending: a + b + c = 120  

money from tickets: 15a + 10b + 12c = 1515  

last constraint: c = 2a --> 2a + 0b - c = 0  

putting this in matrix form:  

[ 1 1 1 120  

15 10 12 1515  

2 0 -1 0 ]  

getting this in row reduced echelon form (rref):  

[ 1 0 0 35  

0 1 0 15  

0 0 1 70 ]  

this relates to our a, b, & c.  

a = 35, meaning 35 adults attended the concert  

b = 15, meaning 15 senior citizens attended the concert  

c = 70, meaning 70 children attended the concert  

from this information we can concluded this musical was a intended for children