Chapter MPS, Problem 4.3MPS

a.

To determine

Organize the data in matrix

Answer to Problem 4.3MPS

  $\left[\begin{array}{ccc}22& 15& 8\\ 20& 18& 12\\ 10& 3& 7\\ 19& 17& 10\end{array}\right]$

Explanation of Solution

Given information:

  $\begin{array}{cccc}Name& Oranges& Grapefruit& \mathrm{Tan}gelos\\ Logan& 22& 15& 8\\ Lizzie& 20& 18& 12\\ Jordan& 10& 3& 7\\ Katherine& 19& 17& 10\end{array}$

Calculation:

Consider the table

  $\begin{array}{cccc}Name& Oranges& Grapefruit& \mathrm{Tan}gelos\\ Logan& 22& 15& 8\\ Lizzie& 20& 18& 12\\ Jordan& 10& 3& 7\\ Katherine& 19& 17& 10\end{array}$

The cost of the oranges is $\$17$ per box.

The cost of the grapefruit is $\$16$ per box.

The cost of the tangelos is $\$27$ per box.

The matrix are as follows

  $\left[\begin{array}{ccc}22& 15& 8\\ 20& 18& 12\\ 10& 3& 7\\ 19& 17& 10\end{array}\right]$

b.

To determine

Find the money raised by each person.

Answer to Problem 4.3MPS

  $\left[\begin{array}{c}830\\ 952\\ 407\\ 856\end{array}\right]$

Explanation of Solution

Given information:

  $\begin{array}{cccc}Name& Oranges& Grapefruit& \mathrm{Tan}gelos\\ Logan& 22& 15& 8\\ Lizzie& 20& 18& 12\\ Jordan& 10& 3& 7\\ Katherine& 19& 17& 10\end{array}$

Calculation:

Consider the table

  $\begin{array}{cccc}Name& Oranges& Grapefruit& \mathrm{Tan}gelos\\ Logan& 22& 15& 8\\ Lizzie& 20& 18& 12\\ Jordan& 10& 3& 7\\ Katherine& 19& 17& 10\end{array}$

The cost of the oranges is $\$17$ per box.

The cost of the grapefruit is $\$16$ per box.

The cost of the tangelos is $\$27$ per box.

The money raised by Logan for each type of fruit is calculated below.

  $\begin{array}{l}\left[\begin{array}{ccc}22& 15& 8\\ 20& 18& 12\\ 10& 3& 7\\ 19& 17& 10\end{array}\right]\times \left[\begin{array}{c}17\\ 16\\ 27\end{array}\right]\\ =\left[\begin{array}{l}374+240+216\\ 340+288+324\\ 170+48+189\\ 323+272+270\end{array}\right]\\ =\left[\begin{array}{c}830\\ 952\\ 407\\ 856\end{array}\right]\end{array}$

Hence, the matrix is $\left[\begin{array}{c}830\\ 952\\ 407\\ 856\end{array}\right]$ .

c.

To determine

Find the total amount of money.

Answer to Problem 4.3MPS

  $\$3045$

Explanation of Solution

Given information:

  $\begin{array}{cccc}Name& Oranges& Grapefruit& \mathrm{Tan}gelos\\ Logan& 22& 15& 8\\ Lizzie& 20& 18& 12\\ Jordan& 10& 3& 7\\ Katherine& 19& 17& 10\end{array}$

Calculation:

Consider the table

  $\begin{array}{cccc}Name& Oranges& Grapefruit& \mathrm{Tan}gelos\\ Logan& 22& 15& 8\\ Lizzie& 20& 18& 12\\ Jordan& 10& 3& 7\\ Katherine& 19& 17& 10\end{array}$

The cost of the oranges is $\$17$ per box.

The cost of the grapefruit is $\$16$ per box.

The cost of the tangelos is $\$27$ per box.

The total amount of money is calculated below.

  $\begin{array}{l}830+952+407+856\\ =3045\end{array}$

Hence, the total amount is $\$3045$ .