Question

kenzie makes quilts from blue and purple pieces of fabric. the diagram shows the ratio of blue pieces to purple pieces.
blue pieces
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 50
b 20

Explanation:

Step1: Determine the ratio

From the diagram, blue pieces (B) : purple pieces (P) = 3 : 5. So total parts = 3 + 5 = 8.

Step2: Solve for Quilt A (Purple pieces)

Let purple pieces be \( p \). Total pieces = 56. The ratio of purple to total is \( \frac{5}{8} \). So \( \frac{p}{56}=\frac{5}{8} \). Cross - multiply: \( 8p = 56\times5 \), \( 8p = 280 \), \( p=\frac{280}{8}=35 \).

Step3: Solve for Quilt B (Total pieces)

Let total pieces be \( t \). Purple pieces = 20. Ratio of purple to total is \( \frac{5}{8} \). So \( \frac{20}{t}=\frac{5}{8} \). Cross - multiply: \( 5t = 20\times8 \), \( 5t = 160 \), \( t=\frac{160}{5}=32 \).

Answer:

Quilt A: 35, Quilt B: 32