Sally is baking cupcakes for her birthday party. The table below shows the total number of sprinkles Sally uses for the number of cupcakes she bakes.

Question

Let c represent the number of cupcakes baked.
Let s represent the total amount of sprinkles used.
Number of Cupcakes Baked
c Total Amount of Sprinkles Used
s
6 120
12 240
18 360

Determine whether each statement is true. Select True or False for each statement.

Statement
True
False
The equation s = 20c represents the relationship between the number of cupcakes baked and the total amount of sprinkles Sally used.
The total amount of sprinkles Sally used is 20 times the number of cupcakes baked.
If Sally baked 24 cupcakes, she will have used 460 total sprinkles.

Answer 1

To evaluate the statements, let's analyze the information provided in the table:

1. For 6 cupcakes, Sally used 120 sprinkles.
2. For 12 cupcakes, she used 240 sprinkles.
3. For 18 cupcakes, she used 360 sprinkles.

From this data, we can derive a ratio of sprinkles to cupcakes:

• For 6 cupcakes: \( \frac{120 \text{ sprinkles}}{6 \text{ cupcakes}} = 20 \text{ sprinkles per cupcake} \)
• For 12 cupcakes: \( \frac{240 \text{ sprinkles}}{12 \text{ cupcakes}} = 20 \text{ sprinkles per cupcake} \)
• For 18 cupcakes: \( \frac{360 \text{ sprinkles}}{18 \text{ cupcakes}} = 20 \text{ sprinkles per cupcake} \)

We can conclude that the relationship between sprinkles and cupcakes is linear, and can be represented by the equation \( s = 20c \).

Now let's evaluate the statements:

1. The equation s = 20c represents the relationship between the number of cupcakes baked and the total amount of sprinkles Sally used.

   • True (the equation accurately represents the relationship).

2. The total amount of sprinkles Sally used is 20 times the number of cupcakes baked.

   • True (this is the assumption derived from the equation \( s = 20c \)).

3. If Sally baked 24 cupcakes, she will have used 460 total sprinkles.

   • To find the total sprinkles for 24 cupcakes, we use the equation \( s = 20c \): \[ s = 20 \times 24 = 480 \text{ sprinkles} \] Since 480 does not equal 460, this statement is:
   • False.

Final answers:

• 1: True
• 2: True
• 3: False

Answer 2

are they correct

Answer 3

Yes, let's confirm the correctness of the evaluations for each statement:

1. The equation \( s = 20c \) represents the relationship between the number of cupcakes baked and the total amount of sprinkles Sally used.

   • True: This statement is correct based on the data provided. Each cupcake requires 20 sprinkles, so the equation accurately describes the relationship.

2. The total amount of sprinkles Sally used is 20 times the number of cupcakes baked.

   • True: This is true because, based on the equation \( s = 20c \), for every cupcake (c), she uses 20 sprinkles (s).

3. If Sally baked 24 cupcakes, she will have used 460 total sprinkles.

   • False: This is incorrect. If we apply the equation \( s = 20c \): \[ s = 20 \times 24 = 480 \text{ sprinkles} \] Since Sally would actually use 480 sprinkles for 24 cupcakes, the statement claiming she used 460 sprinkles is false.

So the evaluations given previously were indeed correct:

• Statement 1: True
• Statement 2: True
• Statement 3: False