The Fox Valley Middle School's colors are purple and white. Heather enjoys making flags for her classmates to wave at school sporting events. She makes 7 purple flags for every 2 white flags.

Question

Complete the table.
Purple flags 7 35
White flags 2 4 6
Graph the data from the table.

Answer 1

To complete the table and find the number of white flags corresponding to the given purple flags, we can establish a relationship based on the ratio of purple to white flags. Heather makes 7 purple flags for every 2 white flags, so the ratio of purple to white flags is 7:2.

To fill in the table, we can express the counts of flags as multiples of the basic ratio:

1. For the existing data:
   • When there are 7 purple flags, there are 2 white flags.
   • When there are 35 purple flags:
     Using the ratio (7 purple : 2 white),
     We can set up a proportion:
     \[ \frac{7}{2} = \frac{35}{x} \]
     Cross-multiplying gives:
     \[ 7x = 70 \quad \Rightarrow \quad x = 10 \]
     So there are 10 white flags corresponding to 35 purple flags.

Now we can fill in the table with values:

| Purple flags | 7 | 14 | 21 | 28 | 35 | |--------------|---|----|----|----|----| | White flags | 2 | 4 | 6 | 8 | 10 |

Graphing the Data

To graph the data from the table, set up a coordinate system:

• X-axis: Number of Purple Flags
• Y-axis: Number of White Flags

Plot the following points based on the completed table:

• (7, 2)
• (14, 4)
• (21, 6)
• (28, 8)
• (35, 10)

Graph Details:

• Mark each point on the graph accordingly.
• Connect the points with a line if you wish to show the continuous nature of the ratio.

The graph will show a straight line, indicating a constant ratio between the number of purple flags and white flags as Heather makes them.