Question

Joanie is making blueberry muffins. The table below shows b, the number of blueberries she used to make m muffins.

Number of Muffins,
m Number of Blueberries,
b
16 144
20 180
24 216
28 252
32 288

If Joanie keeps following this pattern, which of the following equations can she use to find b, the number of blueberries it will take to make m muffins?
A.
b = 9m
B.
m = b + 144
C.
b = m + 144
D.
m = 9b

Answer 1

To find the relationship between the number of muffins, \( m \), and the number of blueberries, \( b \), we can look at the pattern in the provided data.

From the table, we can observe the increase in blueberries as muffins increase:

- For 16 muffins, 144 blueberries are used.
- For 20 muffins, 180 blueberries are used.
- For 24 muffins, 216 blueberries are used.
- For 28 muffins, 252 blueberries are used.
- For 32 muffins, 288 blueberries are used.

To find a relationship between \( b \) and \( m \), let's look at the ratio of blueberries to muffins:

- When \( m = 16 \), \( b = 144 \) ⇒ \( \frac{b}{m} = \frac{144}{16} = 9 \)
- When \( m = 20 \), \( b = 180 \) ⇒ \( \frac{b}{m} = \frac{180}{20} = 9 \)
- When \( m = 24 \), \( b = 216 \) ⇒ \( \frac{b}{m} = \frac{216}{24} = 9 \)
- When \( m = 28 \), \( b = 252 \) ⇒ \( \frac{b}{m} = \frac{252}{28} = 9 \)
- When \( m = 32 \), \( b = 288 \) ⇒ \( \frac{b}{m} = \frac{288}{32} = 9 \)

In all cases, we see that the ratio \( \frac{b}{m} = 9 \).

From this, we can derive the equation:

\[
b = 9m
\]

So among the options given, the correct equation that Joanie can use to find the number of blueberries \( b \) used to make \( m \) muffins is:

**A. \( b = 9m \)**