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

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