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xxMikexx [17]
2 years ago
13

A Community theater sold 63 tickets to the afternon fora total of 444 birr, an adult ticket Cost 8 birr achild ticket cost 4 bir

, 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 tick were sold ? ( Use Gaussian elimination method)
Mathematics
1 answer:
melisa1 [442]2 years ago
8 0

The number of tickets sold are:

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

<h3>How to determine the number of tickets sold to children and seniors?</h3>

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

#SPJ1

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The x =0 and y = 1 are coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2.

<h2>We have to determine</h2>

What are the x- and y- coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2?

<h3>According to the question</h3>

A line segment at points A(2, -3) and B (-4, 9).

The x- and y- coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2 is given by;

\rm x=\dfrac{m}{(m+n)} [x_2- x_1]+ x_1 \\&#10;\\&#10; y=\dfrac{m}{(m+n)} [y_2- y_1]+ y_1 \\&#10;\\

Where \rm x_1 = 2 , \ x_2 =-4, \ y_1 =-3, \ y_2 = 9

Substitute all the values in the formula;

\rm x=\dfrac{m}{(m+n)} [x_2- x_1]+ x_1 \\\\

\rm x=\dfrac{1}{(1+2)} [-4-(2)]+ (2)\\\\ x = \dfrac{1}{3} \times (-6) +2 \\&#10;\\&#10;x = -2+2\\&#10;\\&#10;x=0

\rm y=\dfrac{m}{(m+n)} [y_2- y_1]+ y_1 \\\\ y=\dfrac{1}{(1+2)} [9-(-3)]+ (-3)\\\\&#10;y = \dfrac{1}{3} \times (12) -3\\&#10;\\&#10;y = 4-3\\&#10;\\&#10;y =1

Hence, the x =0 and y = 1 are coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2.

To know more about Coordinates click the link given below.

brainly.com/question/13847533

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