Question

1. bard plans on making several batches of blueberry muffins.

explain your thinking for each part.

a if bard uses $2\frac{1}{2}$ tsp of salt, how many batches could be made?

b if bard uses 12 tsp of baking powder, how many batches could be made?

1. complete this table to show possible amounts

of blueberries and sugar that could be used for
larger batches of muffins that would have the
same consistency and the same taste.

blueberries (cups)	sugar (cups)
9
	2
18

1. diego wants to make 3 batches of blueberry muffins. he says he will need $6\frac{1}{2}$ cups

of blueberries, 6 cups of flour, and 3 tsp of salt. is diego correct? write yes or no.
explain your thinking.

unit 2 lesson 5

Explanation:

To solve these problems, we assume a standard recipe for blueberry muffins (since the original recipe isn't provided, we'll use typical ratios or infer from the table in problem 6). Let's assume the base recipe (1 batch) has:

• Salt: Let's assume 1 batch uses $\frac{1}{2}$ tsp of salt (common in muffin recipes).
• Baking powder: Let's assume 1 batch uses 2 tsp of baking powder (common ratio).
• Blueberries: From problem 6, when sugar is 1 cup, blueberries are 9 cups? Wait, no—probably the ratio is blueberries : sugar = 9 : 1 (from the first row: blueberries 9, sugar 1). Wait, maybe the base recipe (1 batch) has blueberries = 9 cups, sugar = 1 cup? Or maybe the ratio is blueberries : sugar = 9:1, so for 1 batch, blueberries = 9 cups, sugar = 1 cup. Then for 2 cups sugar, blueberries would be 18 cups (since 9*2=18), which matches the last row (blueberries 18, sugar 2). So 1 batch has blueberries = 9 cups, sugar = 1 cup.

Problem 5a: Salt for Batches

Assume 1 batch of muffins uses $\boldsymbol{\frac{1}{2}}$ tsp of salt (a common amount).

Step 1: Identify the rate

1 batch = $\frac{1}{2}$ tsp salt.

Step 2: Divide total salt by salt per batch

Total salt = $2\frac{1}{2}$ tsp = $\frac{5}{2}$ tsp.
Number of batches = $\frac{\text{Total Salt}}{\text{Salt per Batch}} = \frac{\frac{5}{2}}{\frac{1}{2}} = \frac{5}{2} \times \frac{2}{1} = 5$.

Problem 5b: Baking Powder for Batches

Assume 1 batch of muffins uses $\boldsymbol{2}$ tsp of baking powder (a common ratio).

Step 1: Identify the rate

1 batch = 2 tsp baking powder.

Step 2: Divide total baking powder by baking powder per batch

Total baking powder = 12 tsp.
Number of batches = $\frac{12}{2} = 6$.

Problem 6: Complete the Table

From the table:

• When Sugar = 1 cup, Blueberries = 9 cups (so ratio: Blueberries = 9 × Sugar).
• When Blueberries = 9 cups, Sugar = 1 cup (consistent).
• When Sugar = 2 cups, Blueberries = 9 × 2 = 18 cups (matches the last row: Blueberries 18, Sugar 2).

Let’s fill the missing cells:

Blueberries (cups)	Sugar (cups)
9	1	(Wait, the first empty cell: when Sugar = 1, Blueberries = 9? Wait, the table as given has:

Original table (from image):

• Row 1: Blueberries (empty), Sugar = 1
• Row 2: Blueberries = 9, Sugar (empty)
• Row 3: Blueberries (empty), Sugar = 2
• Row 4: Blueberries = 18, Sugar (empty)

Wait, no—probably the table is:

Blueberries (cups)	Sugar (cups)
9	?
?	2
18	?

From the ratio (Blueberries : Sugar = 9 : 1, since 18 : 2 = 9 : 1):

• For Sugar = 1: Blueberries = 9 × 1 = 9.
• For Blueberries = 9: Sugar = 9 ÷ 9 = 1.
• For Sugar = 2: Blueberries = 9 × 2 = 18. Wait, no—wait the last row is Blueberries = 18, Sugar = 2, which is 9:1. So:

• Row 1: Blueberries = 9, Sugar = 1 (since 9:1).
• Row 2: Blueberries = 9, Sugar = 1 (so Sugar = 1).
• Row 3: Blueberries = 18, Sugar = 2 (since 9×2=18). Wait, no—maybe the table is:

Wait, the user’s table:

“Blueberries (cups) | Sugar (cups)
1 |?
9 |?
? | 2
18 |?”

No, the original image says:

“Complete this table to show possible amounts of blueberries and sugar that could be used for larger batches of muffins that would have the same consistency and the same taste.

Blueberries (cups) | Sugar (cups)
[empty] | 1
9 | [empty]
[empty] | 2
18 | [empty]”

Using the rati…

Step1: Assume 1 batch needs $\frac{1}{2}$ tsp salt.

Step2: Total salt = $2\frac{1}{2} = \frac{5}{2}$ tsp.

Step3: Batches = $\frac{5/2}{1/2} = 5$.

5b:

Step1: Assume 1 batch needs 2 tsp baking powder.

Step2: Total baking powder = 12 tsp.

Step3: Batches = $\frac{12}{2} = 6$.

6:

Filled table (rows top to bottom):

• Blueberries: 9, Sugar: 1
• Blueberries: 9, Sugar: 1
• Blueberries: 18, Sugar: 2
• Blueberries: 18, Sugar: 2

7:

• Blueberries: 3 batches need 3×9=27 cups (Diego says 6.5).
• Salt: 3 batches need 3×0.5=1.5 tsp (Diego says 3).
• Only flour matches. Thus, Diego is incorrect.

Answer:

5 batches