Given the expression below
[tex]\frac{3\text{ cakes}}{25\text{ people}}=\frac{\square}{125\text{ people}}[/tex]
Let the unkown quantity be k cakes
[tex]\frac{3\text{ cakes}}{25\text{ people}}=\frac{k\text{ cakes}}{125\text{ people}}[/tex]
To determine the unknown quantity k,
Crossmultiply
[tex]\begin{gathered} \frac{3}{25}=\frac{k}{125} \\ 3\times125=k\times25 \\ 375=25k \\ \text{Divide both sides by 25} \\ \frac{25k}{25}=\frac{375}{25} \\ k=15\text{ cakes} \end{gathered}[/tex]
Hence, the unknown quantity, k, is 15 cakes.
Alternatively
If 3 cakes is shared among 25 people,
The ratio is
[tex]3\colon25[/tex]
Let k cakes be shared among 125 people
The ratio of cakes to the people will be
[tex]k\colon125[/tex]
Which both is equaivalent below
[tex]\begin{gathered} 3\colon25=k\colon125 \\ \frac{3}{25}=\frac{k}{125} \end{gathered}[/tex]
To determine the k cakes shared among 125 people, crossmultiply to eliminate the denominators
[tex]\begin{gathered} \frac{3}{25}=\frac{k}{125} \\ \text{Crossmultiply} \\ 3\times125=k\times25 \\ 375=25k \\ \text{Divide both sides by }25 \\ \frac{25k}{25}=\frac{375}{25} \\ k=15\text{ cakes} \end{gathered}[/tex]
Since, k is the unknown quantity,
Hence, 15 cakes is the unknown quantity
