Question

. A community theater sold 63 tickets to the afternoon performance for a total of 444 Birr. An adult ticket cost 8 Birr, a child ticket cost 4 Birr, and a senior ticket cost 6 Birr. If twice as many tickets were sold to adults as to children and seniors combined, how many of each ticket were sold? (Use Gaussian Elimination Method)​

Answer 1

The number of tickets sold are:

• 30 children tickets were sold
• 33 adult tickets were sold

How to determine the number of tickets sold to children and seniors?

From the question, we have the following parameters:

• Number of tickets = 63
• Total amount = 444 Birr
• Adult ticket = 8 Birr per adult
• Children ticket = 6 Birr per adult

Represent the children tickets with x and adults ticket with y.

So, we have the following system of equations

x + y = 63

6x + 8y = 444

Express the equations as a matrix

x      y

1       1       63

6      8       444

Apply the following transformation

R2 = R2 - 6R1

This gives

x      y

1       1       63

0      2       66

Apply the following transformation

R2 = 1/2R2

x      y

1       1       63

0      1       33

From the above matrix, we have the following system of equations

x + y = 63

y = 33

Substitute y = 33 in x + y = 63

x + 33 = 63

Subtract 33 from both sides of the above equation

x = 30

Hence, 30 children tickets were sold and 33 adult tickets were sold

Read more about Gaussian elimination method at:

brainly.com/question/14529256

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