Tickets to the Senior Class Play cost $3.00 for students, $8.00 for adults, and $5.00 for senior citizens. At Friday night's performance, there were 121 students, 174 adults, and 32 senior citizens. At Saturday night's performance, there were 183 students, 140 adults, and 25 senior citizens. Display this information in matrix form. Then use matrix multiplication to find the ticket sales income for Friday and Saturday night/s performances
the attendance matrix:
121 174 32
183 140 25
the price matrix:
3.00
8.00
5.00
Friday: 121(3) + 174(8) + 32(5) = ....
Satuday: 183(3) + 140(8) + 25(5) = ...
To display the given information in matrix form, we will create a matrix with rows representing the number of different types of individuals (students, adults, senior citizens) and columns representing the two different performances (Friday night, Saturday night).
For Friday night's performance:
- Number of students: 121
- Number of adults: 174
- Number of senior citizens: 32
For Saturday night's performance:
- Number of students: 183
- Number of adults: 140
- Number of senior citizens: 25
Let's create the matrix:
| | Friday Night | Saturday Night |
|----|--------------|----------------|
| Students | 121 | 183 |
| Adults | 174 | 140 |
| Senior Citizens| 32 | 25 |
Now, let's create another matrix for the ticket prices:
| | Students | Adults | Senior Citizens |
|----|----------|--------|-----------------|
| Price | $3.00 | $8.00 | $5.00 |
To find the ticket sales income for each performance, we need to multiply the two matrices.
Matrix multiplication is performed by taking the dot product of each row in the first matrix with each column in the second matrix. Then, the products are summed up to get each element in the resulting matrix.
For example, to find the ticket sales income for Friday night's performance, we multiply the row representing the different types of individuals for Friday night by the respective ticket prices:
(121 * $3.00) + (174 * $8.00) + (32 * $5.00)
Similarly, for Saturday night's performance:
(183 * $3.00) + (140 * $8.00) + (25 * $5.00)
Performing these calculations, we can find the ticket sales income for each night's performance.