select the correct answer.\na fitness center currently has 320 members. monthly membership fees are $45. the…

select the correct answer.\na fitness center currently has 320 members. monthly membership fees are $45. the manager of the fitness center has determined that each time the membership fees increase by $5, approximately 10 members leave and go to a different gym.\nwrite an equation that can be used to find the revenue of the fitness center in dollars, y, after x price increases of $5\n\na. y = - 50x²+3,425x + 14,400\nb. y = - 50x²+2,975x + 14,400\nc. y = - 50x²+2,050x + 14,400\nd. y = - 50x²+1,150x + 14,400

select the correct answer.\na fitness center currently has 320 members. monthly membership fees are $45. the manager of the fitness center has determined that each time the membership fees increase by $5, approximately 10 members leave and go to a different gym.\nwrite an equation that can be used to find the revenue of the fitness center in dollars, y, after x price increases of $5\n\na. y = - 50x²+3,425x + 14,400\nb. y = - 50x²+2,975x + 14,400\nc. y = - 50x²+2,050x + 14,400\nd. y = - 50x²+1,150x + 14,400

Answer

Explanation:

Step1: Find the new membership fee

The initial membership fee is $45 and it increases by $5 for each price - increase $x$. So the new membership fee is $45 + 5x$.

Step2: Find the new number of members

The initial number of members is 320 and 10 members leave for each price - increase $x$. So the new number of members is $320-10x$.

Step3: Calculate the revenue formula

Revenue $y$ is the product of the membership fee and the number of members. So $y=(45 + 5x)(320-10x)$. Expand the right - hand side using the FOIL method: [ \begin{align*} y&=45\times320-45\times10x+5x\times320-5x\times10x\ &=14400-450x + 1600x-50x^{2}\ &=-50x^{2}+(1600 - 450)x+14400\ &=-50x^{2}+1150x + 14400 \end{align*} ]

Answer:

D. $y=-50x^{2}+1150x + 14400$