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

C = 8,420.10/2.9 =

Answer 2

To find the cost of the smaller gold bar, we first need to determine the volume of the smaller bar and then use the given price formula.

We are told that the price of the larger gold bar is $8,420.1 and that its size is a factor of 2.9 times bigger than the smaller bar. Let's assume the length of the side of the larger bar is L.

The volume of the larger bar is given by V = L^3. Similarly, we can calculate the volume of the smaller bar by scaling down the length of its side by a factor of 2.9. Let's call the length of the side of the smaller bar L'.

We have the relationship L' = L/2.9. To find the volume of the smaller bar, substitute this value into the volume formula:
V' = (L/2.9)^3

Now, we know that the price of any gold bar is directly proportional to its volume, and the constant of proportionality is given as c. So, for the larger bar:
P = c * V
$8,420.1 = c * L^3

To find the price of the smaller bar, we substitute the volume V' into the price formula:
P' = c * V'
P' = c * (L/2.9)^3

We need to find the value of P'. Since we don't know the value of the constant of proportionality c, we cannot directly solve for P'. However, we can use the relationship between the larger and smaller bar prices to find the value of P'.

Since the volume of the smaller bar is (1/2.9)^3 = 0.1278 times smaller than the larger bar, we can conclude that the price of the smaller bar will also be 0.1278 times smaller than the price of the larger bar.

Therefore, the cost of the smaller bar in dollars ($) would be:
P' = 0.1278 * $8,420.1

Using a calculator, we can find that the cost of the smaller gold bar is approximately $1,076.32.