1) The equation for each gym modeling the total cost y for a membership lasting

ringearV

ringearV

Answered question

2021-09-16

1) The equation for each gym modeling the total cost y for a membership lasting x months.
Given Gym A charges $10 per month with an additional initiation fee of $100. Gym B charges $0 per month
2) To determine: The time that is more economical for a person to join gym A over gym B.
Given: Gym A lowers its initiation fee to $25. Gym A charges $10 per month with an additional initiation fee of $100. Gym B charges $0 per month.
3) To determine: The time that is more economical for a person to join gym A over gym B.
Given: Gym A charges $10 per month and lowers the initiation fee to $25. Gym B charges $0 per month.

Answer & Explanation

Caren

Caren

Skilled2021-09-17Added 96 answers

1) Concept used:
An equation is formed by multiplying the cost for 1 month with x months and add the additional charges if any.
Calculation:
The equation for Gym A is,
A(x)=10×x+100
=10x+100
Here, x is the number of months and A(x) is the total charge of gym A.
The equation for Gym A is,
B(x)=30×x
=30x
Here, x is the number of months and B(x) is the total charge of gym A.
2) Concept used:
It is more economical for a person to join gym A over gym B if,
A(x)B(x) ......(1)
Calculation:
Substitute the values in equation (1) and simplify for the condition.
A(x)B(x)
10x+10030x
10020x
x5
3) Concept used:
It is more economical for a person to join gym A over gym B if,
A(x)B(x) ......(1)
Calculation:
The equation for Gym A is,
A(x)=10×x+25
=10x+25
Here, x is the number of months and A(x) is the total charge of gym A.
The equation for Gym A is,
B(x)=30×x
=30x
Here, x is the number of months and B(x) is the total charge of gym A.
Substitute the values in equation (1) and simplify for the condition.
A(x)B(x)
10x+2530x
2520x
x2520
=54
=114

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