Question

The cost of attending an amusement park is $10 for children and $20 for adults. On a particular day, the attendance at the amusement park is 30,000 attendees, and the total money earned by the park is $500,000. Use the matrix equation to determine how many children attended the park that day. Use the given matrix equation to solve for the number of children’s tickets sold. Explain the steps that you took to solve this problem.
A matrix with 2 rows and 2 columns, where row 1 is 1 and 1 and row 2 is 10 and 20, is multiplied by matrix with 2 rows and 1 column, where row 1 is c and row 2 is a, equals a matrix with 2 rows and 1 column, where row 1 is 30,000 and row 2 is 500,000.

Answer 1

Based on the figures above, the numbers of children that attended the park that day is 10,000.

What is the matrix equation about?

Fist we have to use the determinant to solve for c and as such:

$\frac{det.\frac{30000}{500000} \frac{1}{20} }{det. \frac{1}{10} \frac{1}{20} }$

=$\frac{30000 x 20 - 500000 x 1}{1 x 20 - 1 x 10}$

= 100000/10

=10,000

Therefore, Based on the figures above, the numbers of children that attended the park that day is 10,000.

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