# Problem of the Week

Problem B and Solution

A Stoney Problem

## Problem

Sela is doing some landscaping, and needs to pave a rectangular space
with an area of \(53.5\) m\(^2\). She plans to use paving stones which
are \(10\,\)cm by \(20\,\)cm, and so each has an area of \(200\,\)cm\(^2\) each. Note that only whole paving
stones will be used.

At the Home Shop, Sela learns that these pavers are sold on pallets
of \(1000\) stones, and she must buy
complete pallets at \(\$499\) each.

How many stones will she need to cover the \(53.5\,\)m\(^2\) area?

How many pallets will she need to buy?

How many stones will be left on the last pallet Sela
uses?

If Sela is able to buy partial pallets, how much would she save
if she only bought the paving stones she needed?

## Solution

One square metre is equivalent to \(100\times 100=10\,000\,\)cm\(^2\), the area Sela needs to pave has area
\(53.5 \times 10\,000 =
535\,000\,\)cm\(^2\). Since each
paving stone has area \(200\,\)cm\(^2\), Sela will need \(535\,000\div 200=2675\) stones.

Since each pallet has 1000 paving stones, Sela needs \(2675\div 1000=2.675\) pallets. However, she
must buy complete pallets, so Sela will need to buy 3 pallets, or 3000
paving stones.

On the last pallet Sela uses, there will be \(3000-2675=325\) paving stones.

Sela would not need to buy the extra 325 paving stones. The 325
paving stones as a fraction of a pallet is \(\frac{325}{1000}=0.325\).

Thus, she would save \(0.325\times\$499\approx\$162.18\).