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The cost of attending an amusement park is $15 for children and $35 for adults on a particular day the attendance at the amusement park is 25,000 attendees and the total money earned by the park is 600,000 use a given matrix equation to solve for the number of children tickets sold

The cost of attending an amusement park is $15 for children and $35 for adults on-example-1
User Sigmund
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2 Answers

2 votes

Final answer:

To determine the number of children's tickets sold, we can set up a system of linear equations with the total number of attendees (25,000) and the total earnings ($600,000) and then solve the matrix equation. This involves finding the inverse of the matrix for the constants (1,1 and 15,35) and applying it to the matrix for the totals (25,000 and 600,000).

Step-by-step explanation:

To solve for the number of children's tickets sold at the amusement park when the total attendance is 25,000 and the total money earned is $600,000, we can use a system of linear equations. We have two unknowns: the number of children, let's call that x, and the number of adults, which we'll call y. We can set up the following equations:

1) x + y = 25,000 (Total attendance)
2) 15x + 35y = 600,000 (Total money earned)

To solve the matrix equation:

A = \[\begin{pmatrix}1 & 1 \\ 15 & 35\end{pmatrix}\], B = \[\begin{pmatrix}25000 \\ 600000\end{pmatrix}\]

The solution is found by using the inverse of matrix A (if it exists) to multiply matrix B. This can be done using various mathematical tools or software.

User Soccerlife
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5.6k points
5 votes

Answer:

13,750

Step-by-step explanation:

Switch values a and d value a 1 and value d 35 and then after that make values b and c negative so turn value b 1 into -1 and turn value c 15 into -15 and then follow this method a×d-(-b)×(-c) so like this 1×35-(15)(1)= 35-15=20 and thats the determinant so then you do put it on a fraction below 1 so like this 1/20 times the top part of the matrix (35 -1 ) and the bottom part of the matrix (-15 1) so mulitply every value by 0.05 so we end up with the top part of the matrix (1.75 -0.05)

and the bottom part of the matrix (-0.75 0.05) and then we multiply them like this

1.75(25,000) + (-0.05)(600,000)= 43,750 - 30,000= 13,750

-0.75(25,000) + 0.05(600,000) = -18,750 + 30,000= 11,250



so the missing matrix is

(13,750 11,250)

so the number of childrens tickets sold is 13,750

User Sachav
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