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Question: At the beginning of the year, Total Assets were $150,000 and Total Liabilities were $70,000. During the year, Assets increased by $30,000 and Liabilities decreased by $10,000. What is the Ending Balance of Owner’s Equity?

Solution:

1. Find Beginning Equity: Use the formula $Assets = Liabilities + Equity$.
   • $150,000 – 70,000 = \$80,000$ (Beginning Equity)
2. Calculate Ending Values:
   • Ending Assets: $150,000 + 30,000 = \$180,000$
   • Ending Liabilities: $70,000 – 10,000 = \$60,000$
3. Solve for Ending Equity:
   • $\$180,000 – \$60,000 = \mathbf{\$120,000}$

Question: How many grams of Water ($H_2O$) are produced when $2.0$ moles of Hydrogen gas ($H_2$) react completely with excess Oxygen? (Molar mass of $H_2O = 18.02$ g/mol).

• Equation: $2H_2 + O_2 \rightarrow 2H_2O$

Solution:

1. Check Molar Ratio: From the balanced equation, $2$ moles of $H_2$ produce $2$ moles of $H_2O$. This is a $1:1$ ratio.
2. Calculate Moles of Product: Since we started with $2.0$ moles of $H_2$, we will produce $2.0$ moles of $H_2O$.
3. Convert to Grams: $\text{Mass} = \text{Moles} \times \text{Molar Mass}$
   • $2.0\text{ mol} \times 18.02\text{ g/mol} = \mathbf{36.04\text{ g}}$

Question: A car starting from rest accelerates at a constant rate of $5.0\text{ m/s}^2$. How far will the car have traveled after $4.0$ seconds?

Solution:

1. Identify Variables: * Initial velocity ($v_i$) = $0$
   • Acceleration ($a$) = $5.0\text{ m/s}^2$
   • Time ($t$) = $4.0\text{ s}$
2. Use Kinematic Equation: $d = v_it + \frac{1}{2}at^2$
3. Calculate: * $d = (0 \times 4) + \frac{1}{2}(5.0)(4.0)^2$
   • $d = 0 + 0.5(5.0)(16)$
   • $d = \mathbf{40\text{ meters}}$

Question: A company’s Cash balance per books is $5,500. The bank statement shows a balance of $5,900. The following items are noted:

1. Deposits in transit: $800
2. Outstanding checks: $1,200
3. Bank service charge: $25
4. Interest earned on account: $15

Solution (Adjusted Cash Balance):

• Bank Side: $\$5,900 (\text{Bank Balance}) + \$800 (\text{DIT}) – \$1,200 (\text{Checks}) = \mathbf{\$5,500}$

Book Side: $\$5,500 (\text{Book Balance}) – \$25 (\text{Service Charge}) + \$15 (\text{Interest}) = \mathbf{\$5,390}$