Question

The average price of a 0.5- carat round diamond is $3700 and the average price of a 0.75- carat diamond is $4950. If the weight and the price of the diamond is linearly related, how much will a 2.5 -carat round diamond cost?

Answer 1

To find the cost of a 2.5-carat round diamond, we can use the concept of proportionality. Setting up a proportion using the average prices of 0.5-carat and 0.75-carat diamonds, we can calculate the cost of a 2.5-carat diamond to be approximately $8192.57.

Step-by-step explanation:

To find the cost of a 2.5-carat round diamond, we can use the concept of proportionality. The average price of a 0.5-carat diamond is $3700, and the average price of a 0.75-carat diamond is $4950. We can set up a proportion to find the cost of a 2.5-carat diamond:

(0.5 carat)/(0.75 carat) = $3700/$4950

To solve for the cost of a 2.5-carat diamond, we can multiply both sides of the equation by 2.5:

(2.5 carat) = ($4950/$3700) * (0.75 carat)

Now we can substitute the values and calculate:

(2.5 carat) = ($4950/$3700) * (0.75 carat) ≈ $8192.57

Therefore, a 2.5-carat round diamond would cost approximately $8192.57.

Answer 2

Since the problem stated the weight and price are in a linear relationship, we can use y=mx+b.

First, let's calculate our slope.

m = (4950-3700)/(0.75-0.5) = 5000

Now, let's solve for b.

3700 = 5000(0.5) + b

Simplify the right side of the equation.

3700 = 2500 + b

Subtract 2500 from both sides

1200 = b

Now our equation looks like this:

y = 5000x + 1200

Let's plug 2.5 in for x to solve for the diamond cost.

y = 5000(2.5) + 1200

Simplify the right side.

y = 13700

The average price of a 2.5 carat diamond is $13700