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3 years ago

Please explain your answer and show your work

Mathematics

1 answer:

MissTica3 years ago

4 0

9514 1404 393

Answer:

A. 6b³

B. 6b +6

C. p = 0.0375(6b³ +b +1)

D. $115.54

Step-by-step explanation:

Given:

3 candles with dimensions b×b×b, b×b×2b, and b×b×3b

with wicks of lengths b+2, 2b+2, 3b+2

wick costs $0.005/cm; wax costs $0.03/cm³

selling price is material cost + 25%

Find:

A. an expression for total volume

B. an expression for total wick length

C. an expression for the purchase price of a set

D. purchase price for a set with base area 64 cm²

Solution:

A. The sum of the volumes of the three candles is ...

v = b³ +2b³ +3b³

v = 6b³

B. The sum of the wick lengths is ...

L = (b +2) +(2b +2) +(3b +2)

L = 6b +6

C. The selling price is 25% more than the cost of materials so is ...

p = (1.25)(0.03×6b³ +0.005×(6b +6)) = 0.225b³ +.0375b +.0375

p = 0.0375(6b³ +b +1)

D. The side of the base is the square root of the base area, so is ...

b = √(64 cm²) = 8 cm

Then the price of a set of candles is ...

p = 0.0375(6·8³ +8 +1) = 0.0375·3081 = 115.54

Purchase price for a candle set with a base area of 64 cm² is $115.54.

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