Chapter 12.7, Problem 2P

To determine

To calculate: The mass in carats of a diamond that cost $4800. if a 1.5 carats diamond costs $2700, also given that the price of a diamond varies directly as the square of its mass in carats.

Answer to Problem 2P

The mass of the diamonds in carats is $m=20$ .

Explanation of Solution

Given information:

The price of a diamond varies directly as the square of its mass in carats.

Let, m = Mass of diamonds in carats

p = Price of diamond

So $p\prec m^2$

Let k be a constant

  $p=k\cdot m^2$...... (1)

Put the value of m and p to get k .

  $p=k\cdot m^2$

  $2700=k\cdot \left(1.5\right){}^2{}^{}$

  $2700=k\cdot \left(2.25\right)$

Solve further to get k ,

  $k=\frac{2700}{2.25}$

  $k=1200$

Now, put the value of k and p in equation (1) to get mass m of the diamond.

  $p=k\cdot m^2$

  $4800=1200\cdot m^2$

  $m=\sqrt{\frac{4800}{1200}}$

  $m=\sqrt{400}$

  $m=20$