Chapter 9.9, Problem 4P

To determine

To calculate:

Value of unknown masses if the known one are $9g,15g,27g$ .

Answer to Problem 4P

Value of unknown masses if the known one are $9g,15g,27g$ is $21g$ .

Explanation of Solution

Given information:

Chemist has three sample of unknown mass and each pair is balance against third sample and one of three known masses.

Calculation:

Let, $x,y,z=$ three unknown masses.

Take two unknown masses and balance it with $3^{rd}$ unknown plus one of the known masses.

There are $3$ such combinations,

  $\begin{array}{l}x+y=z+\mathrm{9...}\left(i\right)\\ x+z=y+\mathrm{15...}\left(ii\right)\\ y+z=x+\mathrm{27...}\left(iii\right)\end{array}$

Solve the equation for $1$

  $z$ : $z=x+y-9$

Substitute into eq. $2$ and $3$ ,

  $\begin{array}{l}x+\left(x+y-9\right)=y+15\\ 2x=24\\ x=12\\ y+\left(x+y-9\right)=x+27\\ 2y=6\\ y=18\end{array}$

Now, substitute to find $z$ ,

  $\begin{array}{l}z=\left(12\right)+\left(18\right)-9\\ z=21\end{array}$

Thus, Value of unknown masses if the known one are $9g,15g,27g$ is $21g$ .