Question

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

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

Step-by-step solution

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:\[ S_{current} = S_{last} \times 1.15 \Rightarrow 3036 = S_{last} \times 1.15 \Rightarrow S_{last} = \frac{3036}{1.15} \S_{last} \approx 2640.00 \]

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:\[ S_{last} = S_{two} \times 1.10 \Rightarrow 2640 = S_{two} \times 1.10 \Rightarrow S_{two} = \frac{2640}{1.10} \S_{two} \approx 2400.00 \]

Key concepts

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’s 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’s 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’s 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.