Jalil used \(125\text{ mm}\) of wire to form an even pentagon. Farid uses a wire that is \(0.5\text{ cm}\) shorter than Jalil's wire to make a square. Find the side lengths, in \(\text{cm}\), of the pentagon and the square.

SOLUTION:
Length of pentagon side that has \(5\) sides.
\(125\text{ mm}\div5=25\text{ mm}\)

Convert mm to cm.
\(25\text{ mm}\div10=2.5\text{ cm}\)

To find the side length of a rectangle, we need to subtract \(0.5\text{ cm}\) from \(125\text{ mm}\).
\(125\text{ mm}\div10=12.5\text{ cm}\)
\(12.5\text{ cm} -0.5\text{ cm}=12.0\text{ cm}\)

A square has \(4\) sides.
So, the length of one side of the square is
\(12.0\text{ cm}\div4=3.0 \text{ cm}\)

How much should be subtracted from \(3\,206\text{ g}\) so that it becomes \(1.507\text{ kg}\) ?

SOLUTION:
Convert \(3\,206\text{ g}\) to \(\text{kg}\).
\(3\,206\text{ g}\div1000=3.206\text{ kg}\)

Mathematical Equation.:
\(3.206\text{ kg}-\Box\text{ kg}=1.507\text{ kg}\)

To find \(\Box\), we will rearrange the equation to
\(3.206\text{ kg}-1.507\text{ kg}=\Box\text{ kg}\)

\(\begin{array}{lr} &\overset{2}{\cancel3}.\overset{11}{\cancel2}\overset{9}{\cancel0}\overset{16}{\cancel6}\text{ kg}\\ -&1.5\,07\,\text{ kg}\\ \hline&1.6\,99\,\text{ kg} \\\hline\end{array}\)

Therefore, \(1.600\text{ kg}\)needs to be subtracted from \(3\,206\text{ g}\) to become \(1.507\text{ kg}\).

A box has \(20\) bottles of mineral water with \(500\,m\ell\) of water in each bottle.
a) ​Find the total volume of mineral water in the box.
​b) All the water are filled equally into jugs that can hold \(1\,\ell\) of liquid. Find the number of jugs that is filled.

SOLUTION
a) Total volume of mineral water in the box.
\(20 \times 500\text{ m}\ell = 10\,000\text{ m}\ell\)

b) Total of jugs filled.
Convert \(10\,000\,m\ell\) to \(\ell\).
\(10\,000\text{ m}\ell\div1\,000=10\,\ell\)

Divide with \(1\,\ell\) to find the number of jugs that can be filled.
\(10\,\ell\div1\,\ell=10\)

So, \(10\) jugs can be filled with mineral water.

Jalil used \(125\text{ mm}\) of wire to form an even pentagon. Farid uses a wire that is \(0.5\text{ cm}\) shorter than Jalil's wire to make a square. Find the side lengths, in \(\text{cm}\), of the pentagon and the square.

SOLUTION:
Length of pentagon side that has \(5\) sides.
\(125\text{ mm}\div5=25\text{ mm}\)

Convert mm to cm.
\(25\text{ mm}\div10=2.5\text{ cm}\)

To find the side length of a rectangle, we need to subtract \(0.5\text{ cm}\) from \(125\text{ mm}\).
\(125\text{ mm}\div10=12.5\text{ cm}\)
\(12.5\text{ cm} -0.5\text{ cm}=12.0\text{ cm}\)

A square has \(4\) sides.
So, the length of one side of the square is
\(12.0\text{ cm}\div4=3.0 \text{ cm}\)

How much should be subtracted from \(3\,206\text{ g}\) so that it becomes \(1.507\text{ kg}\) ?

SOLUTION:
Convert \(3\,206\text{ g}\) to \(\text{kg}\).
\(3\,206\text{ g}\div1000=3.206\text{ kg}\)

Mathematical Equation.:
\(3.206\text{ kg}-\Box\text{ kg}=1.507\text{ kg}\)

To find \(\Box\), we will rearrange the equation to
\(3.206\text{ kg}-1.507\text{ kg}=\Box\text{ kg}\)

\(\begin{array}{lr} &\overset{2}{\cancel3}.\overset{11}{\cancel2}\overset{9}{\cancel0}\overset{16}{\cancel6}\text{ kg}\\ -&1.5\,07\,\text{ kg}\\ \hline&1.6\,99\,\text{ kg} \\\hline\end{array}\)

Therefore, \(1.600\text{ kg}\)needs to be subtracted from \(3\,206\text{ g}\) to become \(1.507\text{ kg}\).

A box has \(20\) bottles of mineral water with \(500\,m\ell\) of water in each bottle.
a) ​Find the total volume of mineral water in the box.
​b) All the water are filled equally into jugs that can hold \(1\,\ell\) of liquid. Find the number of jugs that is filled.

SOLUTION
a) Total volume of mineral water in the box.
\(20 \times 500\text{ m}\ell = 10\,000\text{ m}\ell\)

b) Total of jugs filled.
Convert \(10\,000\,m\ell\) to \(\ell\).
\(10\,000\text{ m}\ell\div1\,000=10\,\ell\)

Divide with \(1\,\ell\) to find the number of jugs that can be filled.
\(10\,\ell\div1\,\ell=10\)

So, \(10\) jugs can be filled with mineral water.