Suppose gold bars are made such that they are cubic. If they are made cubic, then there volume is given by V = L3, where L is the length of a side of the bar. The price of any gold bar is directly proportional to its volume, so the price of the gold is P = c V, where c is some number (a constant) and V is the volume. Suppose a gold bar of some size has a price of $8,420.1 dollars. If another gold bar had sides which were a factor of 2.9 times smaller than the bar which has a price of $8,420.1 dollars, what would be the cost of this smaller bar in dollars ($)?

Question

Suppose gold bars are made such that they are cubic. If they are made cubic, then there volume is given by V = L3, where L is the length of a side of the bar. The price of any gold bar is directly proportional to its volume, so the price of the gold is P = c V, where c is some number (a constant) and V is the volume. Suppose a gold bar of some size has a price of $8,420.1 dollars. If another gold bar had sides which were a factor of 2.9 times smaller than the bar which has a price of $8,420.1 dollars, what would be the cost of this smaller bar in dollars ($)?

Answer 1

Suppose someone invents completely new units where 1 zig = 0.18 zags and 1 zoyear = 0.4 years (typical years, as in 365 days). Convert 585 zag/zoyear to zig/hour.

Answer 2

To find the cost of the smaller gold bar, we need to compare its volume to the volume of the original gold bar and then calculate the price based on the given equation.

Let's start by finding the volume of the original gold bar using the given formula V = L^3, where L is the length of a side of the bar. We have the price P of the original bar as $8,420.1.

P = cV

$8,420.1 = c * (L^3)

Now, let's find the value of c by rearranging the equation:

c = P / V

Substituting the given values:

c = $8,420.1 / (L^3)

Now, let's find the volume of the smaller gold bar. We are told that the sides of the smaller bar are a factor of 2.9 times smaller than the original bar. This means that each side of the smaller bar is 1/2.9 times the length of the original bar.

Let's call the length of the side of the smaller bar L'. Then we have:

L' = L / 2.9

The volume of the smaller bar is V' = (L')^3 = (L/2.9)^3

To find the cost of the smaller bar, we can use the proportionality relationship P = cV. Let's substitute the values we have:

P' = c * V'

P' = c * (L/2.9)^3

Substituting the value of c:

P' = ($8420.1 / (L^3)) * (L/2.9)^3

Simplifying:

P' = $8420.1 * ((L / 2.9)^3 / L^3)

P' = $8420.1 * (1 / 2.9^3)

Now we can calculate the cost of the smaller gold bar. Let's substitute the value of P':

P' = $8420.1 * (1 / 2.9^3) ≈ $8420.1 * 0.1137 ≈ $957.36

Therefore, the cost of the smaller gold bar would be approximately $957.36.