Question

Hello I have to retake a test on Friday! the question is
`(3)/(25) = (?)/(125)`

Answer 1

Given the expression below

`\frac{3\text{ cakes}}{25\text{ people}}=\frac{\square}{125\text{ people}}`

Let the unkown quantity be k cakes

`\frac{3\text{ cakes}}{25\text{ people}}=\frac{k\text{ cakes}}{125\text{ people}}`

To determine the unknown quantity k,

Crossmultiply

`\begin{gathered} (3)/(25)=(k)/(125) \\ 3*125=k*25 \\ 375=25k \\ \text{Divide both sides by 25} \\ (25k)/(25)=(375)/(25) \\ k=15\text{ cakes} \end{gathered}`

Hence, the unknown quantity, k, is 15 cakes.

Alternatively

If 3 cakes is shared among 25 people,

The ratio is

`3\colon25`

Let k cakes be shared among 125 people

The ratio of cakes to the people will be

`k\colon125`

Which both is equaivalent below

`\begin{gathered} 3\colon25=k\colon125 \\ (3)/(25)=(k)/(125) \end{gathered}`

To determine the k cakes shared among 125 people, crossmultiply to eliminate the denominators

`\begin{gathered} (3)/(25)=(k)/(125) \\ \text{Crossmultiply} \\ 3*125=k*25 \\ 375=25k \\ \text{Divide both sides by }25 \\ (25k)/(25)=(375)/(25) \\ k=15\text{ cakes} \end{gathered}`

Since, k is the unknown quantity,

Hence, 15 cakes is the unknown quantity