Let's work through this step by step to determine which statement is true based on the changes in the Smith family's assets and liabilities from 2005 to 2009.
First, we will calculate the total assets and liabilities for both years.
### Assets and Liabilities in 2005:
- Home value: \[tex]$200,000
- Car value: \$[/tex]25,000
- Mortgage: \[tex]$30,000
- Car loan: \$[/tex]8,000
Total Assets in 2005:
[tex]\[
\text{Total Assets} = \text{Home value} + \text{Car value} = 200,000 + 25,000 = 225,000
\][/tex]
Total Liabilities in 2005:
[tex]\[
\text{Total Liabilities} = \text{Mortgage} + \text{Car loan} = 30,000 + 8,000 = 38,000
\][/tex]
### Assets and Liabilities in 2009:
- Home value: \[tex]$180,000
- Car value: \$[/tex]18,000
- Boat value: \[tex]$20,000
- Home equity loan: \$[/tex]18,000
- Personal loan: \[tex]$5,000
Total Assets in 2009:
\[
\text{Total Assets} = \text{Home value} + \text{Car value} + \text{Boat value} = 180,000 + 18,000 + 20,000 = 218,000
\]
Total Liabilities in 2009:
\[
\text{Total Liabilities} = \text{Home equity loan} + \text{Personal loan} = 18,000 + 5,000 = 23,000
\]
### Changes in Assets and Liabilities:
Change in Assets:
\[
\text{Change in Assets} = \text{Total Assets in 2009} - \text{Total Assets in 2005} = 218,000 - 225,000 = -7,000
\]
Change in Liabilities:
\[
\text{Change in Liabilities} = \text{Total Liabilities in 2009} - \text{Total Liabilities in 2005} = 23,000 - 38,000 = -15,000
\]
### Conclusion:
From the computed changes:
- Total assets decreased by \$[/tex]7,000 (from \[tex]$225,000 to \$[/tex]218,000).
- Total liabilities decreased by \[tex]$15,000 (from \$[/tex]38,000 to \$23,000).
Hence, the correct statement is:
a. From 2005 to 2009, both assets and liabilities decreased.
