Question

1. solve: $\frac{6}{5} = \frac{11}{x}$
2. complete the table of equivalent ratios.

ducks	27	18		54
geese		10	25

Explanation:

Question 12

Step1: Cross - multiply the proportion

Given the proportion \(\frac{6}{5}=\frac{11}{x}\), cross - multiplying gives us \(6\times x = 5\times11\).

Step2: Solve for \(x\)

We have the equation \(6x = 55\). To solve for \(x\), we divide both sides of the equation by 6. So \(x=\frac{55}{6}\approx9.17\) (if we want a decimal approximation) or we can leave it as a fraction \(\frac{55}{6}\).

Answer:

\(x = \frac{55}{6}\) (or \(x\approx9.17\))

Question 14

First, we find the ratio of Ducks to Geese from the known values. When Ducks = 18 and Geese = 10, the ratio of Ducks to Geese is \(\frac{18}{10}=\frac{9}{5}\).

For the first column (Ducks = 27, Geese =?)

Let the number of Geese be \(g_1\). Using the ratio \(\frac{27}{g_1}=\frac{9}{5}\). Cross - multiplying: \(9g_1=27\times5\), \(9g_1 = 135\), \(g_1=\frac{135}{9}=15\).

For the third column (Geese = 25, Ducks =?)

Let the number of Ducks be \(d_1\). Using the ratio \(\frac{d_1}{25}=\frac{9}{5}\). Cross - multiplying: \(5d_1=25\times9\), \(5d_1 = 225\), \(d_1=\frac{225}{5}=45\).

For the fourth column (Ducks = 54, Geese =?)

Let the number of Geese be \(g_2\). Using the ratio \(\frac{54}{g_2}=\frac{9}{5}\). Cross - multiplying: \(9g_2=54\times5\), \(9g_2 = 270\), \(g_2=\frac{270}{9}=30\).

The completed table is:

Ducks	27	18	45	54