Question

Answer the following 3 question(s) using the information from the scenario below.

Katrina is looking at banquet halls for her parents’ anniversary party. Moonlight Hall charges a fixed cost of $1000 plus $75 per guest. Riverside Hall charges $1500 plus $50 per guest. Let C represent the total cost, in dollars, and let n represent the number of guests.

Identify the system of linear equations that represents this situation.




Select one
a. Moonlight: C=75n+1000
Riverside: C=50n+1500
b. Moonlight: C=1500−75n
Riverside: C=1000−50n
c. Moonlight: C=1000−75n
Riverside: C=1500−50n
d. Moonlight: C=50n+1000
Riverside: C=75n+1500

What are the coordinates of the solution?

Select one
a. (-20, 0)
b. (20, 0)
c. (20, 2500)
d. (-20, 2500)

Identify the statement that best describes the solution to this linear system.

Select one
a. When there are 20 guests attending, the price is less at the Moonlight Hall.
b. It always costs more to use the Riverside Hall.
c. When there are 20 guests attending the price is $2500.
d. It always costs more to use the Moonlight Hall.

Answer 1

Answer 1: a. Moonlight: C=75n+1000

Riverside: C=50n+1500

Answer 2: c. The solution coordinates are c. (20, 2500)

Answer 3: c. When there are 20 guests attending the price is $2500.

Explanation:

Moonlight Hall:

Fixed cost = $1000

Cost per guest = $75

Cost of 'n' guests = 75
`* n`

Total cost of moonlight hall = Fixed cost + Cost of 'n' guests

`\Rightarrow 1000 + 75 * n`

Riverside Hall:

Fixed cost = $1500

Cost per guest = $50

Cost of 'n' guests = 50
`* n`

Total cost of moonlight hall = Fixed cost + Cost of 'n' guests

`\Rightarrow 1500 + 50 * n`

Hence, Answer 1:

a. Moonlight: C=75n+1000

Riverside: C=50n+1500

Answer 2: Coordinates of solution:

Option c. (20,2500) satisfies both the equation.

When there are 20 number of guests, the cost of both moonlight and riverside hall comes out to be 2500.

Moonlight Hall cost

`75 * 20 + 1000\\\Rightarrow \$2500`

Riverside Hall cost

`50 * 20 + 1500\\\Rightarrow \$2500`

Answer 3: c. When there are 20 guests attending the price is $2500.

The solution is done in Answer 2.

So,

Answer 1: a. Moonlight: C=75n+1000

Riverside: C=50n+1500

Answer 2: c. The solution coordinates are c. (20, 2500)

Answer 3: c. When there are 20 guests attending the price is $2500.