3. a cookie recipe calls for 3 eggs for every 2 dozen cookies.
eccs 3 6 9 12
cookies (dz) 2 4 6 8
a. how many cookies can be made with 12 eggs?
8 cookies
b. how many eggs will be needed for 60 dozen cookies?
4. a developer earns $6.00 for every 21 apps downloaded.
apps 21 42 63 84
$ earned 6 12 18 24
a. how many apps will need to be downloaded in order to earn $84?
b. how much money will the developer earn when 105 apps are downloaded?
use your understanding of ratios and ratio tables to answer the questions below.
5. the relationships between the number of babies to the number of nursery workers is shown in the table below.
dadies workers
5 2
10 4
15 6
20 8
a. what is the ratio of babies to nursery workers?
b. how many nursery workers are required if there are 35 babies?
c. if seven nursery workers are available, then what is the maximum number of babies that they can accept?
6. ms. halpert wrote the table on the board and asked for her students to find the missing value. who found the correct missing value?
# of cups of coffee cost ($)
4 10.60
6 15.90
9 ?
12 31.8
erin: i subtracted 15.90 and 10.60, then added 5.30 and 15.90, so 9 cups of coffee is $21.20.
oscar: i divided 10.60 by 4 and found 1 cup of coffee is $2.65, so 9 cups of coffee is $23.85.

Question

Accepted Answer

### Problem 3a:
# Explanation:
## Step1: Identify the ratio
The recipe has a ratio of eggs to cookies (dozen) as $ 3:2 $.
## Step2: Set up proportion
Let $ x $ be the dozen cookies with 12 eggs. So, $ \frac{3}{2}=\frac{12}{x} $.
## Step3: Solve for $ x $
Cross - multiply: $ 3x = 12\times2 $, $ 3x = 24 $, $ x = 8 $ dozen. Wait, the original answer said 8 cookies, but it should be 8 dozen. But following the steps:
From the table, when eggs are 3, cookies (dozen) are 2. The multiplier from 3 to 12 is $ 12\div3 = 4 $. So cookies (dozen) are $ 2\times4 = 8 $ dozen. If we consider cookies (not dozen), 8 dozen is $ 8\times12 = 96 $ cookies. But the original answer has 8 cookies (maybe a mistake in units, but following the ratio table steps):
Looking at the table, eggs: 3, 6, 9, 12 and cookies (dozen): 2, 4, 6, 8. So when eggs are 12, cookies (dozen) are 8. So the number of cookies (if dozen is considered as the unit in the table) is 8 dozen, but the written answer is 8 cookies (probably a unit error). But following the table's pattern, the answer is 8 (in dozen units, but written as cookies).
# Answer: 8 (assuming the table's unit for cookies is dozen, but the written answer is 8 cookies)

### Problem 3b:
# Explanation:
## Step1: Identify the ratio
Ratio of eggs to cookies (dozen) is $ 3:2 $.
## Step2: Set up proportion
Let $ y $ be the eggs for 60 dozen cookies. $ \frac{3}{2}=\frac{y}{60} $.
## Step3: Solve for $ y $
Cross - multiply: $ 2y = 3\times60 $, $ 2y = 180 $, $ y = 90 $.
# Answer: 90

### Problem 4a:
# Explanation:
## Step1: Identify the ratio
Ratio of apps to money earned is $ 21:6 $ (simplify to $ 7:2 $).
## Step2: Set up proportion
Let $ z $ be the apps for $84. $ \frac{21}{6}=\frac{z}{84} $.
## Step3: Solve for $ z $
Cross - multiply: $ 6z = 21\times84 $, $ 6z = 1764 $, $ z=\frac{1764}{6}=294 $. Or from the table, apps:21, 42, 63, 84 and money:6, 12, 18, 24. Wait, no, the table has apps:21, 42, 63, 84? Wait the table given: apps:21, 42, 63, 84? No, the table for problem 4: apps:21, 42, 63, 84? Wait the table has apps:21, 42, (63), 84 and money:6, 12, 18, 24? Wait no, the money earned for 21 apps is $6, 42 apps is $12, so the ratio is $ \frac{21}{6}=\frac{7}{2} $ apps per dollar. For $84, apps are $ 21\times\frac{84}{6}=21\times14 = 294 $.
# Answer: 294

### Problem 4b:
# Explanation:
## Step1: Identify the ratio
Ratio of apps to money is $ 21:6 $ (simplify to $ 7:2 $).
## Step2: Set up proportion
Let $ w $ be the money for 105 apps. $ \frac{21}{6}=\frac{105}{w} $.
## Step3: Solve for $ w $
Cross - multiply: $ 21w = 105\times6 $, $ 21w = 630 $, $ w = 30 $. Or from the table, the multiplier from 21 to 105 is $ 105\div21 = 5 $. So money is $ 6\times5 = 30 $.
# Answer: 30

### Problem 5a:
# Explanation:
## Step1: Take a pair from the table
Using the first pair: 5 babies and 2 workers. The ratio of babies to workers is $ 5:2 $. Checking other pairs: 10:4 = 5:2, 15:6 = 5:2, 20:8 = 5:2. So the ratio is $ 5:2 $.
# Answer: $ 5:2 $

### Problem 5b:
# Explanation:
## Step1: Use the ratio $ 5:2 $
Let $ m $ be the workers for 35 babies. $ \frac{5}{2}=\frac{35}{m} $.
## Step2: Solve for $ m $
Cross - multiply: $ 5m = 35\times2 $, $ 5m = 70 $, $ m = 14 $.
# Answer: 14

### Problem 5c:
# Explanation:
## Step1: Use the ratio $ 5:2 $
Let $ n $ be the babies for 7 workers. $ \frac{5}{2}=\frac{n}{7} $.
## Step2: Solve for $ n $
Cross - multiply: $ 2n = 5\times7 $, $ 2n = 35 $, $ n = 17.5 $. But we can't have half a baby, so the maximum whole number of babies is 17 (since 17.5 is not a whole number, and 18 babies would need $ \frac{2\times18}{5}=7.2 $ workers, which is more than 7). Wait, but the ratio is $ 5:2 $, so for 7 workers, $ n=\frac{5\times7}{2}=17.5 $. So the maximum number of babies is 17 (if we consider whole numbers) or 17.5 (if we can have half, but in reality, 17).
# Answer: 17.5 (or 17 if whole number)

### Problem 6:
First, find the cost per cup. For 4 cups, cost is $10.60, so per cup is $ 10.60\div4 = 2.65 $.
For 6 cups, cost is $15.90, per cup is $ 15.90\div6 = 2.65 $. So the cost per cup is $2.65.
For 9 cups, cost is $ 2.65\times9 = 23.85 $. Erin's method: $ 15.90 - 10.60 = 5.30 $ (cost for 2 cups), so cost per cup is $ 5.30\div2 = 2.65 $, then 9 cups: from 6 cups (15.90) to 9 cups is 3 more cups. Cost for 3 cups is $ 2.65\times3 = 7.95 $, so total cost $ 15.90 + 7.95 = 23.85 $. Wait, Erin said she subtracted 15.90 and 10.60 (got 5.30), then added 5.30 and 15.90? No, that's wrong. Oscar's method: found cost per cup as $2.65, then 9 cups is $ 2.65\times9 = 23.85 $, which is correct.
# Brief Explanations:
Oscar's method is correct. He found the unit rate (cost per cup) by dividing total cost by number of cups ($ \frac{10.60}{4}=2.65 $ dollars per cup) and then multiplied by 9 to get the cost for 9 cups ($ 2.65\times9 = 23.85 $). Erin's method has an error in the addition step (she added 5.30 and 15.90 which is incorrect, the correct way is to use the unit rate or find the cost for the additional cups correctly).
# Answer: Oscar found the correct missing value.

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QUESTION IMAGE

Question

of cups of coffee cost ($)

Explanation:

Problem 3a:

Step1: Identify the ratio

Step2: Set up proportion

Step3: Solve for \( x \)

Step1: Identify the ratio

Step2: Set up proportion

Step3: Solve for \( y \)

Step1: Identify the ratio

Step2: Set up proportion

Step3: Solve for \( z \)

Answer:

Problem 3b: