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watermelons

by uptowngirl92 » Sun Sep 06, 2009 3:47 am
Two watermelons, A and B, are on sale. Watermelon A has a circumference of 6 inches; watermelon B , 5 inches. If the price of watermelon A is 1.5 times the price of watermelon B , which watermelon is a better buy?

(Assume that the two watermelons are spheres).

A
B
Neither
Both
Impossible to determine

My solution:
Radius of A=3/pi
Radius of B=5/2pi
Cost of B=x$
Cost of A=1.5x=3x/2

For B,x$ can get us a watermelon with a radius of 5/2pi
For A,3x/2$...............................3/pi
= x$......................................2/pi

Comparing,2/pi with 5/2pi we see the latter is larger.Therefore for x dollars B gives us a larger value,hence B.

Please show where i went wrong.
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by eric.gordon884 » Sun Sep 06, 2009 5:47 am
I think it's A.

as you said r(A)=3/pi and r(B)=2.5/pi. This means their volume is 4/3pi*r^3. so

v(A)=4/3pi*(3/pi)^3=4/3pi*27/pi^3=36/pi^2
v(B)=4/3pi*(2.5/pi)^3=4/3pi*15.625/pi^3=~21/pi^2

Now divide their volume by their price p(B)*1.5 and P(B) respectively:

value of A: (36/pi^2) / 1.5*p(B)
value of B: (21/pi^2) / p(B)

eliminate pi^2 and p(B) which occur in both values to get

value of A: 36/1.5= 24 cubic measurement per dollar
value of B: 21 cubic measurement per dollar

A is a better deal- you get more per dollar.
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by engg.manik » Sun Sep 06, 2009 6:12 am
Explanation remains the same

A is the best deal
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