Two spherical canaloupes of the same kind are sold at a fruit and vegetable stand. The circumference of one is 60 cm and that of the other is 50 cm. The larger melon is 1 1/2 times as expensive as the smaller. Which melon is the better buy and why?
change C to radius. C=2PI r
r= C/2PI
Now volume is 4/3 PI r^3
and you are looking for the cost per volume, you want it low.
Melon1: Cost/V=1.5/(4/3 PI (60/2PI)^3)
Melon2: Cost/v= 1/(4/3 PI (50/2PI)^2)
so
comparing cost/volume for melon1 divided by cost/volume for melon2
ratio: 1.5*(50/60)^3 If that is above 1.0, then the best buy has to be melon 2.
If it is below, Melon 1 is the best buy.
Think about that
IF M<RQT=100, WHAT IS M<RST
To determine which melon is the better buy, we need to compare their prices relative to their sizes. We can do this by calculating the prices per unit circumference.
First, let's find the prices of the melons. Let's assume the price of the smaller melon is P.
According to the given information, the larger melon is 1 1/2 times as expensive as the smaller one. Therefore, the price of the larger melon is (1 1/2)P = (3/2)P.
Next, we need to calculate the unit circumference price for each melon.
For the smaller melon with a circumference of 50 cm, the unit price per cm is P/50.
For the larger melon with a circumference of 60 cm, the unit price per cm is (3/2)P/60.
To compare the two melons based on value, we need to determine which melon has a lower unit circumference price. The melon with the lower unit price is considered the better buy.
To compare P/50 and (3/2)P/60, we can simplify the comparison by multiplying each fraction by a common denominator:
The unit price for the smaller melon is P/50 = (P/50)(60/60) = 60P / 2500.
The unit price for the larger melon is (3/2)P/60 = (3P/2)(50/500) = 150P / 3000.
Now, we can compare the unit prices of each melon.
To find the better buy, we need to determine which unit price is lower: 60P / 2500 or 150P / 3000.
To simplify the comparison further, we can divide both sides of the equation by P to remove it from the equation:
(60 / 2500) = (150 / 3000).
After simplifying, we find that 0.024 = 0.05, which is false.
Since the equation is false, we can conclude that there was an error in the calculations or the given information.
Therefore, we cannot determine which melon is the better buy based on the provided information.