In February 2023, Euros and Japanese Yens had the following exchange rate: 1 EUR = 143 JPY. How many Euros is 2860 Japanese Yens?[br][br]We can solve this problem by using proportion equations. Let us create the following table first:[br][table] [tr][br] [td][b]Euros[/b][br][/td][br] [td][b]Yens[/b][br][/td][br][/tr][br] [tr][br] [td]1 EUR [/td][br] [td]143 JPY[/td][br][/tr][br] [tr][br] [td][math]x[/math][br][/td][br] [td]2860 JPY[/td][br][/tr][br][/table][br]We have a proportion equation:[br][br][math]\frac{1 \, \mathrm{EUR}}{x} = \frac{143 \, \mathrm{JPY}}{2860 \, \mathrm{JPY}}[/math][br][br]We can cancel the JPY units on the right-hand side:[br][br][math]\frac{ \textcolor{red}{1 \, \mathrm{EUR}} }{ \textcolor{blue} x} = \frac{ \textcolor{blue}{143} }{ \textcolor{red}{2860} }[/math][br][br]Now, let us perform the cross multiplication by multiplying the red terms, and the blue terms:[br][br][math]1 \, \mathrm{EUR} \cdot 2860 = x \cdot 143,[/math][br][br]that is,[br][br][math]2860 \, \mathrm{EUR} = 143x . [/math][br][br]We can swap the left-hand side and the right-hand side to obtain:[br][br][math]143x = 2860 \, \mathrm{EUR} . [/math][br][br]To solve this equation, we divide both sides by the coefficient of [math]x[/math], that is, we divide both sides by 143:[br][br][math]x = \frac{2860 \, \mathrm{EUR}}{143} = 20 \, \mathrm{EUR} . [/math][br][br]Therefore, 5330 Japanese Yens corresponds to 20 Euros.

We know that the average velocity ([math]v[/math]) can be calculated as the ratio of the distance travelled ([math]s[/math]) and the time spent ([math]t[/math]), that is, [math]v = \frac{s}{t}[/math]. If a car travels with a velocity of 80 km/h, how long does it take to travel 500 km?[br][br][b]Method 1:[/b] traditional equation solving.[br][br][math]\large \begin{array}{rcll}[br]v & = & \frac{s}{t} & | \cdot t \\[br]v\cdot t & = & s & | : v \\[br]t & = & \frac{s}{v} \\[br]t & = & \frac{500 \, \mathrm{km}}{80 \, \mathrm{km/h}} \\[br]t & = & 6{,}25 \, \mathrm{h} . [br]\end{array}[br][/math][br][br][b]Method 2:[/b] proportion equation.[br][br]Let us write [math]v = \frac{v}{1}[/math] to obtain a proportion equation:[br][br][math]\large \begin{array}{rcll}[br]\frac{ \textcolor{red} v}{ \textcolor{blue} 1} & = & \frac{\textcolor{blue} s}{ \textcolor{red} t} .[br]\end{array}[br][/math][br][br]Now, we can proceed by performing the cross multiplication:[br][br][math]\large \begin{array}{rcll}[br]v \cdot t & = & 1 \cdot s & | : v \\[br]t & = & \frac{s}{v} \\[br]t & = & \frac{500 \, \mathrm{km}}{80 \, \mathrm{km/h}} \\[br]t & = & 6{,}25 \, \mathrm{h} . [br]\end{array}[br][/math][br][br]It takes 6,25 hours to travel 500 kilometers.