Question

which table shows a constant of proportionality of 2 for the ratio of string instruments to percussion instruments? percussion string 3 2 6 4 9 6 percussion string 5 2 10 4 15 6 percussion string 1 2 2 4 3 6 percussion string 4 2 8 4 12 6

Explanation:

Step1: Calculate ratio for first table

For first table:

• When percussion = 3, string = 2, ratio \(=\frac{2}{3}\)
• When percussion = 6, string = 4, ratio \(=\frac{4}{6}=\frac{2}{3}\)
• When percussion = 9, string = 6, ratio \(=\frac{6}{9}=\frac{2}{3}\)

Step2: Calculate ratio for second table

For second table:

• When percussion = 5, string = 2, ratio \(=\frac{2}{5}\)
• When percussion = 10, string = 4, ratio \(=\frac{4}{10}=\frac{2}{5}\)
• When percussion = 15, string = 6, ratio \(=\frac{6}{15}=\frac{2}{5}\)

Step3: Calculate ratio for third table

For third table:

• When percussion = 1, string = 2, ratio \(=\frac{2}{1} = 2\)
• When percussion = 2, string = 4, ratio \(=\frac{4}{2}=2\)
• When percussion = 3, string = 6, ratio \(=\frac{6}{3}=2\)

Step4: Calculate ratio for fourth table

For fourth table:

• When percussion = 4, string = 2, ratio \(=\frac{2}{4}=\frac{1}{2}\)
• When percussion = 8, string = 4, ratio \(=\frac{4}{8}=\frac{1}{2}\)
• When percussion = 12, string = 6, ratio \(=\frac{6}{12}=\frac{1}{2}\)

Answer:

The third table (with percussion values 1, 2, 3 and string values 2, 4, 6) shows a constant of proportionality of 2 for the ratio of string instruments to percussion instruments.