Question

a recipe for one batch of blueberry muffins uses the ingredients shown in the table. use this information for problems 4–7.

1. complete the double number line representing the amounts of sour cream and flour.

sour cream (cups)
flour (cups)

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

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
38

ingredient
amount
blueberries
2\\(\frac{1}{4}\\) cups
sour cream
1 cup
salt
\\(\frac{1}{2}\\) tsp
flour
2 cups
baking powder
3 tsp
sugar
1 cup

blueberries (cups)
sugar (cups)
1
9
2
18

Explanation:

Problem 5a

Step1: Identify salt per batch

One batch uses $\frac{1}{2}$ tsp of salt.

Step2: Divide total salt by per - batch salt

Total salt used is $2\frac{1}{2}$ tsp, which is $\frac{5}{2}$ tsp. Number of batches $=\frac{5}{2}\div\frac{1}{2}=\frac{5}{2}\times2 = 5$.

Problem 5b

Step1: Identify baking powder per batch

One batch uses 3 tsp of baking powder.

Step2: Divide total baking powder by per - batch baking powder

Total baking powder used is 12 tsp. Number of batches $=12\div3 = 4$.

Problem 6

First, find the ratio of blueberries to sugar in one batch. From the recipe, blueberries are $2\frac{1}{4}=\frac{9}{4}$ cups and sugar is 1 cup. So the ratio of blueberries to sugar is $\frac{9}{4}:1 = 9:4$? Wait, no, wait. Wait, in the table for problem 6, when sugar is 1 cup, blueberries should be $2\frac{1}{4}$ cups? Wait, no, let's re - examine. Wait, the original recipe: blueberries are $2\frac{1}{4}$ cups, sugar is 1 cup. So the ratio of blueberries to sugar is $2\frac{1}{4}:1=\frac{9}{4}:1 = 9:4$? Wait, no, the table in problem 6 has blueberries and sugar. Let's see the given values. When blueberries are 9, what's sugar? When blueberries are $2\frac{1}{4}$ (which is $\frac{9}{4}$) for 1 cup of sugar. So the multiplier: $9\div\frac{9}{4}=9\times\frac{4}{9}=4$? No, that can't be. Wait, maybe the ratio is blueberries to sugar is $2\frac{1}{4}:1=\frac{9}{4}:1$, so for sugar = 1, blueberries = $\frac{9}{4}$? But the table has blueberries as 9, sugar as? Wait, maybe I made a mistake. Wait, the table in problem 6:

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

From the original recipe, 1 batch has blueberries $2\frac{1}{4}=\frac{9}{4}$ cups and sugar 1 cup. So the ratio of blueberries to sugar is $\frac{9}{4}:1$. So:

• When sugar = 1, blueberries = $\frac{9}{4}=2\frac{1}{4}$
• When blueberries = 9, sugar = $9\div\frac{9}{4}=4$ (because $\frac{9}{4}\times4 = 9$)
• When sugar = 2, blueberries = $\frac{9}{4}\times2=\frac{9}{2}=4\frac{1}{2}$
• When blueberries = 18, sugar = $18\div\frac{9}{4}=18\times\frac{4}{9}=8$

So the completed table is:

Blueberries (cups)	Sugar (cups)
9	4
$4\frac{1}{2}$	2
18	8

Problem 7

Step1: Calculate required blueberries for 3 batches

One batch needs $2\frac{1}{4}=\frac{9}{4}$ cups of blueberries. For 3 batches, blueberries needed: $3\times\frac{9}{4}=\frac{27}{4}=6\frac{3}{4}$ cups. Diego says $6\frac{1}{2}$ cups, which is wrong.

Step2: Calculate required flour for 3 batches

One batch needs 2 cups of flour. For 3 batches, flour needed: $3\times2 = 6$ cups (this is correct).

Step3: Calculate required salt for 3 batches

One batch needs $\frac{1}{2}$ tsp of salt. For 3 batches, salt needed: $3\times\frac{1}{2}=\frac{3}{2}=1\frac{1}{2}$ tsp. Diego says 3 tsp, which is wrong.
Since two of the three quantities are wrong, Diego is not correct.

Answer:

5 batches