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Chapter 6: Problem 32

Bill's Bikes has sold \(\$ 3036.00\) worth of merchandise this month. That is a \(15 \%\) increase over last month. And last month saw a \(10 \%\) increase over the month before. How much merchandise did Bill's Bikes sell two months ago? A. \(\$ 3021\) B. \(\$ 3011\) C. \(\$ 2640\) D. \(\$ 2400\)

Short Answer

Expert verified
Two months ago, Bill's Bikes sold approximately \$ 2400.00 in merchandise.

Step by step solution

01

Calculate Last Month's Sales

First, determine last month's sales by considering the current month's sales and the 15% increase. Let last month's sales be denoted as \( S_{last} \). Given \( S_{current} = 3036 \), and knowing this is a 15% increase over last month:\[ S_{current} = S_{last} \times 1.15 \Rightarrow 3036 = S_{last} \times 1.15 \Rightarrow S_{last} = \frac{3036}{1.15} \S_{last} \approx 2640.00 \]
02

Determine Sales Two Months Ago

Now, using the sales from last month, calculate the sales from two months ago by considering the 10% increase. Let the sales two months ago be denoted as \( S_{two} \). Given \S_{last} \approx 2640, and knowing this represents a 10% increase over the previous month:\[ S_{last} = S_{two} \times 1.10 \Rightarrow 2640 = S_{two} \times 1.10 \Rightarrow S_{two} = \frac{2640}{1.10} \S_{two} \approx 2400.00 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

sales calculations
We use the formula:
  • Sales_next_month = Sales_this_month * (1 + percentage_increase)

For a decrease, a similar formula can be used:
  • Sales_next_month = Sales_this_month * (1 - percentage_decrease)

By rearranging these formulas, we can find the initial sales figure from any given month's sales.
percentage increase
To find last month's sales:
  • Divide this month鈥檚 sales by 1.15, because this represents the equation Sales_this_month = Sales_last_month * (1 + 0.15).

Consider the relationship in the problem:
  • (Sales_last_month * 1.15 = Sales_this_month)
By rearranging this equation:
  • Sales_last_month = Sales_this_month / 1.15

After we find last month's sales, a similar process can be followed for the month before last.
algebraic equations
For the given problem, we derived:
  • Sales_last_month = Sales_current / 1.15

Using the result, we can set up the next equation:
  • Sales_two_months_ago = Sales_last_month / 1.10
Remember, always isolate the variable of interest and solve step by step.
problem-solving
1. Identify the knowns and unknowns: This month鈥檚 sales ( Sales_this_month=3036)
  • Identify the increases (15% and 10%)

2. Translate words into an equation: Using algebraic formulas, set up equations given the increases
3. Solve the equations: Calculate last month鈥檚 sales first, then go back another month to find the sales two months ago.

  • Practice and break down similar problems into these steps will make solving them easier each time.

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Most popular questions from this chapter

Marisa pays \(6.2 \%\) Social Security tax, \(1.45 \%\) Medicare, and \(14 \%\) federal income tax withholding each pay period. How much is left after taxes from a paycheck of \(\$ 718.15\) ? A. \(\$ 707.74\) B. \(\$ 670.81\) C. \(\$ 617.61\) D. \(\$ 562.67\)

To be considered a periodical under the post office's rules, a magazine must have no more than \(25 \%\) advertising content. The present issue of the magazine that Aram manages has 172 pages but is \(28.5 \%\) ads. How many pages must Aram convert from ads to nonadvertising content to meet the post office's requirement? A. 4 B. 5 C. 6 D. 7

Last year 1,320,000 people visited the state fair. This year \(1,544,400\) visited. What percentage increase or decrease was this, to the nearest whole percent? A. 15 B. 16 C. 17 D. 18

After paying a \(6 \frac{1}{4} \%\) sales tax, Jerome paid \(\$ 135.20\) for a set of Blu-ray discs that listed for \(\$ 149.70\) but was on sale at a discount. To the nearest whole percent, what was the discount on the set before sales tax? A. \(6 \%\) B. \(7 \%\) C. \(14 \%\) D. \(15 \%\)

Elita bought a scarf on sale for \(\$ 14.49\) after a \(16 \%\) discount. What was the scarf's original price? A. \(\$ 17.25\) B. \(\$ 17.34\) C. \(\$ 12.88\) D. \(\$ 14.95\) The following question contains a blank marked \begin{tabular}{|l|l|} \hline Select... & . Beneath the blank is \(a\) set of choices. \\ \hline \end{tabular} Indicate the choice that is correct and belongs in the blank. (Note: On the real GED* test, the choices will appear as \(a\) "drop-down"menu. When you click on a choice, it will appear in the blank.)
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