Please explain your answer and show your work

9514 1404 393

  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.