Question

model it
complete the problems about representing proportional relationships.
2 ramona makes catnip toys for the cats at the shelter. she puts the same amount of catnip in each toy. ramona makes 4 toys with 12 grams of catnip.
a. complete the equivalent ratio table to show how many toys ramona can make with different amounts of catnip.
number of toys | catnip (grams)
0 | 0
1 | 3
2 | 6
3 | 9
4 | 12
5 | 15
b. describe the relationship between the number of grams of catnip and the number of toys.
c. what is the unit rate for grams of catnip per toy? how can ramona find the number of grams of catnip she needs to make a certain number of toys?
d. write an equation to show the number of grams of catnip, g, ramona needs to make t toys.

Explanation:

Part a: Completing the Ratio Table

Step 1: Find the unit rate

From the given data, 4 toys use 12 grams of catnip. So the unit rate (grams per toy) is $\frac{12}{4} = 3$ grams per toy. This means 1 toy uses 3 grams of catnip.

Step 2: Calculate for 0 toys

If 1 toy uses 3 grams, 0 toys will use $0\times3 = 0$ grams.

Step 3: Calculate for 2 toys

For 2 toys, the catnip used is $2\times3 = 6$ grams.

Step 4: Calculate for 9 grams of catnip

To find the number of toys for 9 grams, we divide the total grams by the unit rate: $\frac{9}{3}=3$ toys.

Step 5: Calculate for 5 toys

For 5 toys, the catnip used is $5\times3 = 15$ grams.

So the completed table is:

Number of Toys	Catnip (grams)
1	3
2	6
3	9
4	12
5	15

Part b: Describing the Relationship

The number of grams of catnip and the number of toys have a proportional relationship. As the number of toys increases, the grams of catnip used increases at a constant rate. Specifically, the grams of catnip is 3 times the number of toys (since each toy uses 3 grams of catnip).

Step 1: Find the unit rate

Using the given data (4 toys, 12 grams), the unit rate (grams per toy) is calculated as $\frac{12}{4}=3$ grams per toy.

Step 2: Explain how to find catnip for toys

To find the number of grams of catnip needed for a certain number of toys, Ramona can multiply the number of toys by the unit rate (3 grams per toy). For example, if she wants to make $t$ toys, the grams of catnip $g = 3\times t$.

Answer:

The grams of catnip is directly proportional to the number of toys, with a constant rate of 3 grams per toy (i.e., grams of catnip = 3 × number of toys).

Part c: Unit Rate and Finding Catnip for Toys