The table shows the amount budgeted and the amount spent for each of three accounts in a certain company. For which of these accounts did the amount spent differ from the amount budgeted by more than 6 percent of the amount budgeted?
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To quickly compare fractions, you can use benchmarks. For Payroll, \( \frac{7}{110} \), we know \(6%\) is \(0.06\). Is \(7/110>0.06\)? Multiply by 110: Is \(7>0.06 \times 110\)? Is \(7>6.6\)? Yes. For Insurance, is \(160/2500>0.06\)? Multiply by 2500: Is \(160>0.06 \times 2500\)? Is \(160>150\)? Yes. This can be faster than finding the exact percentage.
Step 1: Understanding the Concept:
We need to calculate the percent difference for each account relative to its budgeted amount and determine if that difference is greater than 6%. Step 2: Key Formula or Approach: Percent Difference = \(\frac{|\text{Amount Spent} - \text{Amount Budgeted}|}{\text{Amount Budgeted}} \times 100%\)
We will calculate this for each of the three accounts. Step 3: Detailed Explanation: Payroll:
Difference = \(|117,000 - 110,000| = 7,000\).
Budgeted = 110,000.
Percent Difference = \(\frac{7,000}{110,000} \times 100% = \frac{7}{110} \times 100% \approx 6.36%\).
Since \(6.36%>6%\), Payroll qualifies. Taxes:
Difference = \(|42,000 - 40,000| = 2,000\).
Budgeted = 40,000.
Percent Difference = \(\frac{2,000}{40,000} \times 100% = \frac{2}{40} \times 100% = \frac{1}{20} \times 100% = 5%\).
Since \(5% \ngtr 6%\), Taxes does not qualify. Insurance:
Difference = \(|2,340 - 2,500| = 160\).
Budgeted = 2,500.
Percent Difference = \(\frac{160}{2,500} \times 100% = \frac{16}{250} \times 100% = \frac{1600}{250}% = 6.4%\).
Since \(6.4%>6%\), Insurance qualifies. Step 4: Final Answer:
The accounts where the spending differed from the budget by more than 6% are Payroll and Insurance. This corresponds to option (D).
