## Problem Solving

 5.4 Problem Solving

LENGTH
 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 $$12.0\text{ cm}\div4=3.0 \text{ cm}$$

MASS
 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 $$1.507\text{ kg}$$.

VOLUME OF LIQUID
 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.