Question

The table represents the number of cups of flour needed, f,
based on the number of batches of muffins made, b.

Batches of Muffins (b)
Cups of Flour (f)

2
3

313
5

6
9


Which equation represents the amount of flour needed, f,
to bake b
batches of muffins?
Responses

f=1.5b
f is equal to 1 point 5 b

f=103b
f is equal to 10 thirds b

f=23b
f is equal to 2 thirds b

f=3b

Answer 1

To find the equation that represents the relationship between the number of batches of muffins (b) and the cups of flour needed (f), we will first analyze the data points given:

1. For 2 batches (b = 2), cups of flour needed (f) is 3.
2. For 3 batches (b = 3), cups of flour needed (f) is 5.
3. For 6 batches (b = 6), cups of flour needed (f) is 9.

Now, let's calculate the ratio of cups of flour to batches:

- From the first point: \( \frac{3}{2} = 1.5 \)
- From the second point: \( \frac{5}{3} \) (approximately 1.67)
- From the third point: \( \frac{9}{6} = 1.5 \)

The first and third values suggest that \( f = 1.5b \) holds true for those points.

To express this as an equation:

\[
f = 1.5b
\]

This corresponds to the first response option:

**f = 1.5b**

So the equation that best represents the amount of flour needed to bake \( b \) batches of muffins is \( f = 1.5b \).