lesson 15 | session 3
4 a box holds 12 cups of cereal. this amount is equivalent to 16 servings.
part a use a model to show the number of cups of cereal per serving and the number of servings per cup of cereal.
part b explain how your model shows each rate.
part c if you want to know how many cups of the cereal are in a box that holds 24 servings, which rate would you use? explain.
5 math journal a farm stand sells 3 quarts of peaches for $15. use a model to write a rate for this situation. what does this rate tell you?
(there is an image of a cereal box labeled fit flakes with 12 cups cereal 16 servings on it)

Question

Accepted Answer

### Problem 4 - Part A
# Explanation:
## Step 1: Find cups per serving
To find cups per serving, divide total cups by total servings. So, $12 \div 16 = \frac{12}{16} = \frac{3}{4}$ cups per serving.
## Step 2: Find servings per cup
To find servings per cup, divide total servings by total cups. So, $16 \div 12 = \frac{16}{12} = \frac{4}{3}$ servings per cup.
A model like a tape diagram can be used: draw a tape for 12 cups divided into 16 equal parts (each part is $\frac{3}{4}$ cup) for cups per serving. For servings per cup, draw a tape for 16 servings divided into 12 equal parts (each part is $\frac{4}{3}$ servings).

### Problem 4 - Part B
# Brief Explanations:
For cups per serving: The tape diagram for 12 cups split into 16 sections shows each section (serving) has $\frac{3}{4}$ cup, as $12\div16 = \frac{3}{4}$. For servings per cup: The tape for 16 servings split into 12 sections shows each section (cup) has $\frac{4}{3}$ servings, as $16\div12=\frac{4}{3}$.
# Answer:
Cups per serving: $\frac{3}{4}$ cup per serving (shown by dividing 12 - cup tape into 16 parts). Servings per cup: $\frac{4}{3}$ servings per cup (shown by dividing 16 - serving tape into 12 parts).

### Problem 4 - Part C
# Brief Explanations:
To find cups in 24 servings, use cups per serving rate ($\frac{3}{4}$ cup per serving). Multiply servings (24) by cups per serving: $24	imes\frac{3}{4}=18$ cups. This rate relates servings to cups, so multiplying servings by cups per serving gives total cups.
# Answer:
Use cups per serving rate ($\frac{3}{4}$ cup per serving). Explanation: To find total cups from servings, multiply number of servings by cups per serving (since cups per serving tells how many cups are in one serving, so scaling by number of servings gives total cups).

### Problem 5
# Explanation:
## Step 1: Find the rate
To find the rate, we can find dollars per quart or quarts per dollar. Let's find dollars per quart: divide total cost by total quarts. So, $\$15\div3$ quarts $= \$5$ per quart.
A model like a double - number line can be used: label one line for quarts (0, 1, 2, 3) and the other for dollars (0, 5, 10, 15). The point where 3 quarts meet 15 dollars shows that 1 quart corresponds to 5 dollars.
## Step 2: Interpret the rate
The rate of $\$5$ per quart tells us that each quart of peaches costs $\$5$.
# Answer:
The rate is $\$5$ per quart (or $\frac{1}{5}$ quart per dollar). The rate $\$5$ per quart tells us the cost of one quart of peaches is $\$5$.

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QUESTION IMAGE

Question

Explanation:

Problem 4 - Part A

Step 1: Find cups per serving

Step 2: Find servings per cup

Problem 4 - Part B

Answer:

Problem 4 - Part C