olivier offers music lessons for $18 per half - hour lesson. students must enroll for a weekly class…

olivier offers music lessons for $18 per half - hour lesson. students must enroll for a weekly class. looking at his records for the past five years, he determines that for each price increase of $1, he loses about 4 students (and it follows, 4 weekly lessons). at the current rate, olivier has 63 students enrolled. for a change in price of x dollars, which of the following functions correctly models oliviers weekly revenue, in dollars? choose 1 answer: a w(x)=(x + 18)(x - 4) b w(x)=0.5(x + 18)(x - 4) c w(x)=(18 + x)(63 - 4x) d w(x)=0.5(18 + x)(63 - 4x)

olivier offers music lessons for $18 per half - hour lesson. students must enroll for a weekly class. looking at his records for the past five years, he determines that for each price increase of $1, he loses about 4 students (and it follows, 4 weekly lessons). at the current rate, olivier has 63 students enrolled. for a change in price of x dollars, which of the following functions correctly models oliviers weekly revenue, in dollars? choose 1 answer: a w(x)=(x + 18)(x - 4) b w(x)=0.5(x + 18)(x - 4) c w(x)=(18 + x)(63 - 4x) d w(x)=0.5(18 + x)(63 - 4x)

Answer

Explanation:

Step1: Determine the new price

The original price per half - hour lesson is $18. With a price change of $x$ dollars, the new price per half - hour lesson is $18 + x$ dollars.

Step2: Determine the new number of students

The original number of students is 63. For each $1$ dollar increase in price, 4 students are lost. So for a price increase of $x$ dollars, the number of students lost is $4x$. The new number of students is $63-4x$.

Step3: Calculate the weekly revenue

Weekly revenue is the product of the price per lesson and the number of students. Since the price is for a half - hour lesson and we are calculating weekly revenue (and each student takes one weekly class which is one half - hour lesson), the revenue function $W(x)=(18 + x)(63 - 4x)$.

Answer:

C. $W(x)=(18 + x)(63 - 4x)$