Respuesta :
Using linear functions, it is found that Ginny must attend at least 13 events to make the premier member package cost less.
What is the complete question?
The complete question is given as follows:
"Ginny wants to join a local dance club that has dance events every week. There are two membership options available: Ginny may become a premier member by paying a fee of $150 per year and attend an unlimited number of dances. Ginny may become a regular member by paying a fee of $50 and then pay $8 per dance she attends. How many dances must Ginny attend such that becoming a premier member will cost less than becoming a regular member? "
What is a linear function?
A linear function is modeled in slope-intercept form 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 this problem, we have that:
- The flat fee is the intercept.
- The cost per dance is the slope.
Hence the functions for each option are given as follows:
- P(x) = 150.
- R(x) = 50 + 8x.
Being a premier member will cost less when:
P(x) < R(x).
Hence:
150 < 50 + 8x
8x > 100
x > 100/8
x > 12.5 -> at least 13 events.
Ginny must attend at least 13 events to make the premier member package cost less.
More can be learned about linear functions at https://brainly.com/question/24808124
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