SOLUTION: Olivia designs and sells necklaces. The materials for each necklace cost $4. She sells an average of 40 necklaces a week for $8. She would like to raise the price, but for each $0.

Question 1049535: Olivia designs and sells necklaces. The materials for each necklace cost $4. She sells an average of 40 necklaces a week for $8. She would like to raise the price, but for each $0.50 increase she would lose four sales each week.
a) write an expression to represent the price of each necklace.
b) write an expression to represent the number of necklaces sold per week
c) use your answers in a) and b) to write an expression that represents Olivia's revenue from the sales of her necklaces.
d) Write an expression to represent the cost of materials for the necklaces
e) Use your answers from c) and d) to write an equation for Olivia's profit
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Olivia designs and sells necklaces. The materials for each necklace cost $4. She sells an average of 40 necklaces a week for $8. She would like to raise the price, but for each $0.50 increase she would lose four sales each week.
a) write an expression to represent the price of each necklace.
Ans: p(x) = (800/40) + 50x = 20 + 50x cents
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b) write an expression to represent the number of necklaces sold per week
Ans: s(x) = 40 - 4x
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c) use your answers in a) and b) to write an expression that represents Olivia's revenue from the sales of her necklaces.
R(x) = price * # of units sold = (20+50x)(40-4x)
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d) Write an expression to represent the cost of materials for the necklaces
C(x) = 4(40+x)
e) Use your answers from c) and d) to write an equation for Olivia's profit
P(x) = R(x)-C(x) = (20+50x)(40-4x)-(160+4x) in cents
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Cheers,
Stan H.
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