Edvin records pet adoptions at an animal shelter. He notices that for every 3

Question

dog adoptions, there are 2
cat adoptions.

Which equations describe the number of cat adoptions, c,
based on dog adoptions, d,
at the animal shelter?

Select all that apply.

Responses

c=3d
c is equal to 3 d

23d=c
2 thirds d is equal to c

c=2d
c is equal to 2 d

c2=d3
c over 2 is equal to d over 3

d=23c

Answer 1

To determine the relationship between dog adoptions (d) and cat adoptions (c) given the ratio of 3 dog adoptions for every 2 cat adoptions, we can set up the following proportion:

\[ \frac{d}{c} = \frac{3}{2} \]

From this, we can derive equations that express c in terms of d.

1. Starting from the proportion: \[ 2d = 3c \] Rearranging gives: \[ c = \frac{2}{3}d \]

This means that for every 3 dog adoptions, we have 2 cat adoptions.

Now, let's examine the provided options:

1. c = 3d: This implies 3 cat adoptions for every dog adoption and is incorrect.
2. \(\frac{2}{3}d = c\): Reflects \(c = \frac{2}{3}d\), which is correct.
3. c = 2d: This implies 2 cat adoptions for every dog adoption and is incorrect.
4. \(\frac{c}{2} = \frac{d}{3}\): This can be rearranged to confirm the ratio (3c = 2d), so it is correct.
5. d = \frac{2}{3}c: This correctly reflects the inverse relationship based on the original ratio (3 dog adoptions for every 2 cat adoptions), so it is correct.

Thus, the correct equations that describe the relationship between cat adoptions (c) and dog adoptions (d) based on the given information are:

• \(\frac{2}{3}d = c\)
• \(\frac{c}{2} = \frac{d}{3}\)
• \(d = \frac{2}{3}c\)