Chapter 8, Problem 9MCQ

To determine

The number of ways, the shoes can be organized so that same number of shoes on each shelf, at least 4 pairs of shoes per shelf and at least 2 shelves of shoes.

Answer to Problem 9MCQ

The shoes can be displayed as:

  $\left(2,12\right),\left(3,8\right),\left(4,6\right),\left(6,4\right)$

Explanation of Solution

Given:

A fashion clerk is organizing 24 pairs of shoes for sales display.

First evaluate the factor of the 24:

  $24=1,2,3,4,6,8,12,24$

The pairs of the factors which satisfy the conditions:

  $\left(2,12\right),\left(3,8\right),\left(4,6\right),\left(6,4\right)$

Here, the first number is representing the number of shelves and the second number is denoting the number of shoes on each shelf.

As, the minimum number of the shelf possible is 2, hence, the factor (1,24) is not considered.

Thus, the shoes can be displayed as:

  $\left(2,12\right),\left(3,8\right),\left(4,6\right),\left(6,4\right)$

So that, each shelf has same number of the shoes.