Select ALL the correct answers.
Sandy has four boxes filled with pink ribbons and yellow ribbons. The table shows the number of pink and yellow ribbons in each box.

Box Number
Pink Ribbons
Yellow Ribbons
1
4
5
2
16
20
3
12
15
4
36
45

A fifth box has pink and yellow ribbons in the same proportion as Sandy’s first four boxes. Which tables could represent box number 5?

 
Box Number
Pink Ribbons
Yellow Ribbons
5
8
10
 
Box Number
Pink Ribbons
Yellow Ribbons
5
40
60
 
Box Number
Pink Ribbons
Yellow Ribbons
5
32
45
 
Box Number
Pink Ribbons
Yellow Ribbons
5
24
30


To solve this, we need to determine the proportion of pink to yellow ribbons in Sandy's first four boxes and then see which of the given box options maintains that same proportion.

### Step 1: Calculate the ratio of pink to yellow ribbons in each box

- **Box 1**: \( \frac{4}{5} = 0.8 \)
- **Box 2**: \( \frac{16}{20} = 0.8 \)
- **Box 3**: \( \frac{12}{15} = 0.8 \)
- **Box 4**: \( \frac{36}{45} = 0.8 \)

All the boxes have the same proportion of pink to yellow ribbons, which is \( 0.8 \) or \( \frac{4}{5} \).

### Step 2: Check each option to see if it has the same proportion:

1. **Box 5 (8 pink, 10 yellow)**:
   \( \frac{8}{10} = 0.8 \), which is correct.

2. **Box 5 (40 pink, 60 yellow)**:
   \( \frac{40}{60} = \frac{2}{3} = 0.6667 \), which is not correct.

3. **Box 5 (32 pink, 45 yellow)**:
   \( \frac{32}{45} \approx 0.7111 \), which is not correct.

4. **Box 5 (24 pink, 30 yellow)**:
   \( \frac{24}{30} = 0.8 \), which is correct.

### Conclusion:
The correct answers are:
- **Box 5 (8 pink, 10 yellow)**
- **Box 5 (24 pink, 30 yellow)**

Would you like further clarification on any part of the process?

Here are five related questions for practice:
1. If Box 5 had 48 pink ribbons, how many yellow ribbons should it have to maintain the same ratio?
2. What is the ratio of yellow ribbons to total ribbons in Box 3?
3. How many total ribbons are there in all four boxes combined?
4. If another box had 64 pink ribbons, what should the number of yellow ribbons be?
5. What would the ratio be if a box had 20 pink ribbons and 35 yellow ribbons?

**Tip:** Whenever comparing ratios, always simplify to ensure they are equivalent!

Sandy has four boxes filled with pink ribbons and yellow ribbons. The table shows the number of pink and yellow ribbons in each box.

Box Number
Pink Ribbons
Yellow Ribbons
1
4
5
2
16
20
3
12
15
4
36
45

A fifth box has pink and yellow ribbons in the same proportion as Sandy’s first four boxes. Which tables could represent box number 5?

Box Number
Pink Ribbons
Yellow Ribbons
5
8
10

Box Number
Pink Ribbons
Yellow Ribbons
5
40
60

Box Number
Pink Ribbons
Yellow Ribbons
5
32
45

Box Number
Pink Ribbons
Yellow Ribbons
5
24
30

Learn how to solve a proportion problem involving pink and yellow ribbons across multiple boxes. The problem focuses on finding equivalent ratios and applying them to a new scenario. Suitable for students in Grades 5-7.

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