Answered

The Reed and the Merrill families are comparing their utility costs for the past month. The following is a list of the appliances that the families are using to make their comparisons:




Reed Family Appliances		Merrill Family Appliances


\begin{tabular}[t]{l}
Gas range

5 cents per day
&


Electric range

13 cents per day
\\

\hline


Gas dryer - 1 load per day

10 cents per load
&


Gas dryer - 1 load per day

10 cents per load
\\

\hline


Electric water heater

90 cents per day
&


Gas water heater

40 cents per day
\\

\hline


Typical later model refrigerator

16 cents per day
&


Energy Star-labeled refrigerator

12 cents per day
\\

\hline

\end{tabular}



Assuming that the families use the same appliances in the same way, who spends more to run these appliances in a given 30-day period and by how much?


AThe Reed family spends \$13.80 more than the Merrill family.
BThe Reed family spends \$0.46 more than the Merrill family.
CThe Merrill family spends \$58.80 more than the Reed family.

Verified Answer :

  • Calculate Reed daily cost: \(5 + 10 + 90 + 16 = 121\) cents.
  • Calculate Merrill daily cost: \(13 + 10 + 40 + 12 = 75\) cents.
  • Calculate the 30-day difference: \(30 \times (121 - 75) = 30 \times 46 = 1380\) cents.
  • Convert to dollars: \(\$13.80\), so the final answer is \(\boxed{a}\).

Explanation

  1. Calculating Daily Expenses

To determine which family spends more on utilities over a 30-day period, we first calculate the daily cost for each family based on the provided data.
The Reed family's daily expenses consist of:

  • Gas range: \(5\) cents
  • Gas dryer: \(10\) cents
  • Electric water heater: \(90\) cents
  • Refrigerator: \(16\) cents

Summing these gives the daily total for the Reed family: \(C_R = 5 + 10 + 90 + 16 = 121\) cents.

The Merrill family's daily expenses consist of:

  • Electric range: \(13\) cents
  • Gas dryer: \(10\) cents
  • Gas water heater: \(40\) cents
  • Refrigerator: \(12\) cents

Summing these gives the daily total for the Merrill family: \(C_M = 13 + 10 + 40 + 12 = 75\) cents.

  1. Calculating 30-Day Total Expenses

Next, we calculate the total expenses for each family over a 30-day period.
For the Reed family: \(30 \times 121 = 3630\) cents.
For the Merrill family: \(30 \times 75 = 2250\) cents.
Comparing the two totals, we see that the Reed family spends more than the Merrill family.
The difference in cents is: \(3630 - 2250 = 1380\) cents.

  1. Converting and Final Conclusion

Finally, we convert the difference from cents to dollars by dividing by \(100\):
\(1380 \div 100 = 13.80\).
Therefore, the Reed family spends \(\$13.80\) more than the Merrill family. This corresponds to option (a).

Examples

In real life, comparing utility costs is a practical way to manage household budgets. By breaking down daily expenses of various appliances—like refrigerators or water heaters—one can identify which devices are the most expensive to run and where potential savings can be made. For example, if you compare the efficiency of an electric versus a gas water heater as seen here, you can make informed decisions about future home upgrades that lead to significant long-term financial savings.

Related Questions