227k views
4 votes
SKATING PARTYYou are planning a birthday party for your youngerbrother at a skating rink. The cost of admission is $3. 50 per adult and $2. 25 perchild, and there is a limit of 20 people. Youhave $50 to spend. Use an inversematrix to determine how many adults and how many childrenyou can invite

1 Answer

4 votes

Answer:

To determine how many adults and children you can invite to the skating party within the given budget, we can use an inverse matrix. Let's set up the problem as a system of equations.

Let:

x = number of adults to invite

y = number of children to invite

We can form two equations based on the given information:

Equation 1: Cost of admission for adults: 3.50x

Equation 2: Cost of admission for children: 2.25y

We also have the constraint that the total number of people (adults and children) should not exceed 20:

x + y ≤ 20

To solve this system of equations, we can represent it in matrix form:

[3.50 2.25] [x] [50]

[y]

Let's call the coefficient matrix A, the variable matrix X, and the constant matrix B:

A = [3.50 2.25]

X = [x]

[y]

B = [50]

To find the solution, we can use the inverse matrix of A:

A^-1 = [a b]

[c d]

where a, b, c, and d are the elements of the inverse matrix.

The solution is given by X = A^-1 * B:

X = [a b] [50]

[c d]

Multiplying A^-1 and B, we get:

[a b] [50] [solution for x]

[c d] = [solution for y]

Once we determine the values for x and y, we will know how many adults and children you can invite within the given budget.

Please note that I have used approximate values for the admission costs.

User Kabdulla
by
9.0k points

Related questions

1 answer
4 votes
90.8k views
asked Jul 7, 2021 81.3k views
Katsiaryna asked Jul 7, 2021
by Katsiaryna
7.4k points
2 answers
1 vote
81.3k views