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Answer:
A. 6b³
B. 6b +6
C. p = 0.0375(6b³ +b +1)
D. $115.54
Step-by-step explanation:
<u>Given</u>:
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%
<u>Find</u>:
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
<u>Solution</u>:
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.
