Chapter 11, Problem 57RE

To determine

To find: The size of box.

Answer to Problem 57RE

The numbers of small, medium and large boxes to be brought are $1,5\text{ and 2}$ respectively.

Explanation of Solution

Given information:

The given, small box contains $1$ dozen oatmeal raisin and $1$ dozen chocolate chip.

The medium box contains $2$ dozen oatmeal raisin, $2$ dozen chocolate chip and $1$ dozen shortbread.

The large box contains 2 dozen oatmeal raisin, $2$ dozen chocolate chip and $3$ dozen shortbread.

Calculation:

Calculate the boxes,

Let, $x$ is the number of small box, $y$ is the number of medium box, and $z$ is the number of large box.

The first equation represents the total number of raisin,

  $x+2y+2z=15$ .

The second equation represents the total number of chocolate chips,

  $x+y+2z=10$

The third equation represents the total number of shortbread,

  $y+3z=11$ .

The system of three linear equation.

  $\begin{array}{c}x+2y+2z=15\\ x+y+2z=10\\ y+3z=11\end{array}$

Subtract the second equation from the first.

  $\begin{array}{c}x+2y+2z=15\\ x+y+2z=10\\ y=5\end{array}$

Substitute the value of $y$ in the third equation.

  $\begin{array}{l}5+3z=11\\ 3z=6\\ z=2\end{array}$

Substitute the value of $y\text{ and }z$ in second equation.

  $\begin{array}{c}x+5+2\left(2\right)=10\\ x+9=10\\ =10-9\\ =1\end{array}$

Therefore, the numbers of small, medium and large boxes to be brought are $1,5\text{ and 2}$ respectively.