Chapter 9.9, Problem 3P

To determine

To calculate:

Mass of each diamond.

Answer to Problem 3P

Mass of each diamond are $2,4$ and $8$

Explanation of Solution

Given information:

  $3$ large diamonds are weighed in pairs, masses of the pairs are found to be $6$ carats, $10$ carats and $12$ carats.

Calculation:

Let the mass of the diamonds be $x,y,z$

Then equation will be,

  $\begin{array}{l}x+y=\mathrm{6...}\left(i\right)\\ y+z=\mathrm{10...}\left(ii\right)\\ x+z=\mathrm{12...}\left(iii\right)\end{array}$

Now, subtract eq. $\left(i\right)$ from eq. $\left(iii\right)$ to get $z-y=\mathrm{6...}\left(iv\right)$

Add eq. $\left(iv\right)$ and eq. $\left(ii\right)$ .

To get $2z=16$

Thus, $z=8,y=2,x=4$

Thus, Mass of each diamond are $2,4$ and $8$ respectively.