Kenzie makes quilts from blue and purple pieces of fabric. The diagram shows the ratio of blue pieces to purple pieces.
A tape diagram with 2 tapes of unequal lengths. The first tape has 3 equal parts. A curved bracket above the first tape is labeled Blue pieces. The second tape has 5 equal parts of the same size as in the first tape. A curved bracket below the second tape is labeled Purple pieces.
The table shows the number of purple pieces and the number of total pieces that Kenzie will make on two of her quilts.
Based on the ratio, complete the missing values in the table.
Quilt	Purple pieces	Total pieces
\[A\]	
\[56\]
\[B\]	
\[20\]	


Let's break down the problem and use the given ratio of blue to purple pieces to solve it. The tape diagram indicates that:

- The number of **blue pieces** is divided into 3 equal parts.
- The number of **purple pieces** is divided into 5 equal parts.
  
This means the ratio of **blue to purple** pieces is **3:5**.

### Total Pieces Formula
The total number of pieces in any quilt is the sum of blue and purple pieces. Using the ratio, we know that for every 3 blue pieces, there are 5 purple pieces. This gives us a ratio of total pieces to purple pieces:

\[
\text{Total Pieces} : \text{Purple Pieces} = (3 + 5) : 5 = 8 : 5
\]

Now, let's apply this to the given quilts.

### Quilt A
We know that quilt A has **56 purple pieces**. Using the ratio of **total pieces to purple pieces (8:5)**, we can set up a proportion:

\[
\frac{\text{Total Pieces}}{\text{Purple Pieces}} = \frac{8}{5}
\]

Substituting the value of purple pieces for quilt A:

\[
\frac{\text{Total Pieces}}{56} = \frac{8}{5}
\]

Now, solve for the total number of pieces in quilt A:

\[
\text{Total Pieces} = 56 \times \frac{8}{5} = 56 \times 1.6 = 89.6
\]

Since the number of pieces must be a whole number, we round it to **90** total pieces for quilt A.

### Quilt B
For quilt B, we know there are **20 total pieces**. Using the total-to-purple ratio, we set up another proportion:

\[
\frac{8}{5} = \frac{20}{\text{Purple Pieces}}
\]

Now, solve for the number of purple pieces in quilt B:

\[
\text{Purple Pieces} = 20 \times \frac{5}{8} = 12.5
\]

Again, since the number of pieces must be a whole number, we round it to **12** purple pieces for quilt B.

### Completed Table

| Quilt | Purple Pieces | Total Pieces |
|-------|---------------|--------------|
| A     | 56            | 90           |
| B     | 12            | 20           |

Let me know if you need further clarification or a more detailed explanation.

### Related Questions
1. What would the number of blue pieces be for Quilt A?
2. What is the ratio of purple to total pieces in general?
3. How many blue pieces are in Quilt B?
4. If there were 64 purple pieces in Quilt A, how many total pieces would there be?
5. How do you calculate the number of blue pieces based on total pieces?

### Tip
When working with ratios, always remember to express them in their simplest form before applying them to specific values.

Kenzie makes quilts from blue and purple pieces of fabric. The diagram shows the ratio of blue pieces to purple pieces. A tape diagram with 2 tapes of unequal lengths. The first tape has 3 equal parts. A curved bracket above the first tape is labeled Blue pieces. The second tape has 5 equal parts of the same size as in the first tape. A curved bracket below the second tape is labeled Purple pieces. The table shows the number of purple pieces and the number of total pieces that Kenzie will make on two of her quilts. Based on the ratio, complete the missing values in the table. Quilt A [56], Quilt B [20].

Learn how to solve a ratio problem involving blue and purple quilt pieces. This problem shows the ratio of 3 blue pieces to 5 purple pieces, and guides you through completing the table of quilt A with 56 purple pieces and quilt B with 20 total pieces. Suitable for Grades 5-7.

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