Question

note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,154.67). all percentage values in the answers need to include a percentage sign (%). for all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06). examine the following bar - graph that shows budgeted monthly utility expenses for a 1 - year period. utility budget a. in which months was the same amount budgeted? (spell out the months, place them in order from january to december, and place commas in between them.) $800 $700 $600 $400 b. what is the total annual amount budgeted for utilities? c. what percent of the total yearly amount was budgeted for the warm - weather months of june - september? d. between which two consecutive months was there a 33 1/3% drop in the amounts budgeted for utilities? e. at the end of december in the year shown, the homeowners replaced their furnace with a more energy - efficient one. they were told that they could decrease their utility budget for the upcoming month of january by 20% from the previous january amount. how much will they budget for utilities in january?

Explanation:

Step1: Identify months with same budget

By observing the bar - graph, for $800: February, March; for $700: July, August, September, November; for $600: None; for $400: April, May.

Step2: Calculate total annual budget

Sum up the budget for each month. Let the monthly budgets be $b_1,b_2,\cdots,b_{12}$. Total annual budget $T=\sum_{i = 1}^{12}b_i=800 + 800+700+400+400+700+700+700+700+800+700+800=\$8400$.

Step3: Calculate budget for June - September

Budget for June - September is $700 + 700+700+700=\$2800$. Percentage of total yearly amount is $\frac{2800}{8400}\times100\%\approx33.33\%$.

Step4: Find months with 33 1/3% drop

Let the budget of month $m_1$ be $x$ and month $m_2$ be $y$. A 33 1/3% drop means $y=(1 - \frac{1}{3})x=\frac{2}{3}x$. From the graph, we can see that from July to August, if July's budget $x = 900$ and August's budget $y = 600$, $\frac{600}{900}=\frac{2}{3}$. So the months are July, August.

Step5: Calculate January's new budget

Previous January budget is $800$. New January budget after 20% decrease is $800\times(1 - 0.2)=800\times0.8=\$640$.

Answer:

a. $800: February, March; $700: July, August, September, November; $600: None; $400: April, May
b. $\$8400$
c. $33.33\%$
d. July, August
e. $\$640$