Problem Solving

If 12 cans of soda cost x dollars, then how much will y cans of soda cost at this rate, in cents?

$$A)\ \frac{3xy}{25}$$
$$B)\ \frac{xy}{12}$$
$$C)\frac{3y}{25x}$$
$$D)\frac{25xy}{3}$$
$$E)\frac{12y}{x}$$

The OA is D.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

Hello swerve.

We have 12 cans of soda cost x $, that is to say, $$12\cdot s=x\ dollars\ \leftrightarrow\ s=\frac{x\ }{12}dollars.$$ Now, y cans of soda will cost $$y\cdot s=y\cdot\frac{x}{12}dollars\ \leftrightarrow\ y\cdot s=\frac{xy}{12}dollars.$$ Now, we have to convert this to cents.

Using that 1$ =100cents we will get $$\frac{xy\ dollars}{12}=\frac{xy\ dollars}{12}\cdot\frac{100\ cents}{1\ dollar}=\frac{25xy}{3}.$$ So, the correct answer is D .

I hope this may help you.

I'm available if you'd like a follow up.

Regards,