A piano artist will give a recital. His managing company gave him three options on
how he can be paid for his upcoming performance.
Option 1
Receive $9,500 for the
performance plus 5% of all
ticket sales.
O Option 1
Payment Option Plans
O Option 2
O Option 3
O All options are equal.
Option 2
Receive $8,000 for the
performance plus 10% of all
ticket sales.
Option 3
Each ticket will cost $20.00 dollars.
If the pianist needs to earn $13,000, which option will need the fewest ticket sales to
meet his goal?
Receive $4,500 for the
performance plus 15% of
all ticket sales.

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joaobezerra joaobezerra · Answer 1 · 2022-08-24T16:03:19+02:00

Using linear functions, it is found that option 2 will need the fewest amount of ticket sold.

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For each option, we have that:

For option 1, the earnings with x ticket sales is given by:

y = 9500 + 0.05x.

With y = 13000, we find the amount of tickets that have to be sold to earn $13,000, hence:

13000 = 9500 + x

x = 3,500 tickets

For option 2, the earnings with x ticket sales is given by:

y = 8000 + 2x.

Hence:

13000 = 8000 + 2x

2x = 5000

x = 2,500

x = 2,500 tickets;

For option 3, the earnings with x ticket sales is given by:

y = 4500 + 3x.

13000 = 4500 + 3x

3x = 8500

x = 8500/3

x = 2,833 tickets.

Hence option 2 will need the fewest amount of ticket sold.

More can be learned about linear functions at https://brainly.com/question/24808124

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