Question

a fabric store has 3 yards of polka - dot fabric for every 6 yards of striped fabric. there are 48 yards of striped fabric in the store.
(a) build a diagram that shows the number of yards of polka - dot fabric and the number of yards of striped fabric in the store. make sure to do these steps.

• drag to adjust the number of sections in the diagram below.
• fill in the input box to show how many yards are in each section.

number of yards in each section:
diagram: total yards, with two sections (one for polka - dot fabric, one for striped fabric) and a drag to build the diagram prompt, and labels yards of polka - dot fabric and yards of striped fabric
(b) using the diagram, find the number of yards of polka - dot fabric in the store.
input box for answer yards

Explanation:

Step1: Find yards per section

The ratio of polka - dot to striped is 3:8. For striped fabric, total yards are 48. Let each section be \(x\) yards. The number of sections for striped is 8 (from the ratio 3:8), so \(8x = 48\). Solving for \(x\), we divide both sides by 8: \(x=\frac{48}{8}=6\).

Step2: Find polka - dot yards

The number of sections for polka - dot is 3 (from the ratio 3:8). Each section is 6 yards, so the number of yards of polka - dot fabric is \(3\times6 = 18\).

Answer:

(a) The number of yards in each section is 6.
(b) The number of yards of polka - dot fabric in the store is 18.