Question

If \(y\) grams is equivalent to \(d\) drams, of the following, which best represents the relationship between \(y\) and \(d\) ? A) \(y=1.8 d\) B) \(d=1.8 y\) C) \(y d=1.8\)

Short answer

The correct relationship between y grams and d drams is \(y = 1.8 d\).

Step-by-step solution

Analyze each option

Let's go through each given option and see if it's a valid relationship between grams and drams: A) \(y = 1.8 d\) B) \(d = 1.8 y\) C) \(y d = 1.8\)

Reason through option A

\(\$y = 1.8 d\)\) means that y grams (the mass in grams) is equal to 1.8 times the quantity in drams (d). This seems like a possible option since it is implying that there is a direct proportionality between grams and drams.

Reason through option B

\(\$d = 1.8 y\)\) means that d drams (the mass in drams) is equal to 1.8 times the quantity in grams (y). This option is less likely than option A because it would mean that drams are "heavier" than grams, whereas grams are the heavier unit of mass.

Reason through option C

\(\$y d = 1.8\)\) means that the product of y grams and d drams is equal to 1.8. This does not make sense for the relationship between the two units of mass.

Choose the correct relationship

Based on the analysis in steps 2-4, Option A (\(\$y = 1.8 d\)\)) is the relationship that best represents the connection between y grams and d drams. This is because it demonstrates that the mass in grams is directly proportional to the mass in drams, and grams are a heavier unit of mass than drams.