over the period of a year, sams net worth increased. which of the following could be true? a. sams assets…
over the period of a year, sams net worth increased. which of the following could be true? a. sams assets and liabilities decreased by the same amount. b. sams assets and liabilities increased by the same amount. c. sams assets increased by more than his liabilities. d. sams assets decreased by more than his liabilities. please select the best answer from the choices provided
Answer
Explanation:
Step1: Recall net - worth formula
Net worth is calculated as Net Worth = Assets - Liabilities.
Step2: Analyze option a
If assets ($A$) and liabilities ($L$) decrease by the same amount $x$, the new net worth $NW_{new}=(A - x)-(L - x)=A - x - L + x=A - L$, which is the same as the original net worth.
Step3: Analyze option b
If assets and liabilities increase by the same amount $y$, the new net worth $NW_{new}=(A + y)-(L + y)=A + y - L - y=A - L$, which is the same as the original net worth.
Step4: Analyze option c
If assets increase by $m$ and liabilities increase by $n$ where $m>n$, the new net worth $NW_{new}=(A + m)-(L + n)=A - L+(m - n)$. Since $m - n>0$, the net worth increases.
Step5: Analyze option d
If assets decrease by $p$ and liabilities decrease by $q$ where $p>q$, the new net worth $NW_{new}=(A - p)-(L - q)=A - L-(p - q)$. Since $p - q>0$, the net worth decreases.
Answer:
C. Sam's assets increased by more than his liabilities.