Problem 34 - Prealgebra

Question

To make a profit, a store tries to sell an item for more than it paid for the item. The increase in price is called the markup. Suppose a store purchases paint brushes for ?8 each. Find the markup if the brushes are sold for \(15 \%\) over the price paid for them.

Step-by-Step Solution

Answer

The markup is ?1.2.

Step 1: Understand the Given Values

We are given the cost of paint brushes, which is ?8 each. The store wants to increase the sell price by 15% of the cost price to find the markup.

Step 2: Calculate the Markup Percentage

First, identify the markup percentage, which is 15% of ?8.

Step 3: Convert Percentage to Decimal

To find 15% of ?8, we convert 15% to a decimal. This is done by dividing by 100, so 15% becomes 0.15.

Step 4: Calculate the Markup Amount

Multiply the cost of ?8 by the decimal. So, the markup is calculated as:\[ 8 \times 0.15 = 1.2 \]This means the markup amount is ?1.2.

Step 5: Finalize the Markup

Ensure the calculations make sense: increasing the cost of ?8 by ?1.2 results in a sale price of ?9.2 if starting from the cost price only. However, this exercise only focuses on calculating the markup itself.

Key Concepts

Profit Calculation

Profit calculation is a key part of running a successful business. When a store sells an item for more than it was purchased, it creates a profit.
Profit can be calculated simply by subtracting the cost price from the selling price.

• If a store owner buys paint brushes for ?8 and sells them at ?9.2, the profit would be the difference between these two amounts.
• In mathematical terms, profit = selling price - cost price.

Using the paint brush example, if the selling price is ?9.2 and the cost price is ?8, then:\[\text{Profit} = 9.2 - 8 = 1.2\]Understanding profit calculation is crucial, as it informs how much a business makes above its spending on goods.

Percentage Increase

Percentage increase measures how much a price has risen compared to the original amount. It helps retailers set prices that will provide a profit.
It is calculated by taking the difference between the new price and the original price, divided by the original price. The result is then multiplied by 100 to get a percentage.

• In this exercise, the store decided to increase the price by 15%.
• That means if the original cost price of the paint brush is ?8, 15% of 8 is added on top of that.

This can be calculated as follows:\[\text{Percentage Increase} = \left(\frac{\text{New Price} - \text{Original Price}}{\text{Original Price}}\right) \times 100\]For the paintbrush, the increase amount can be separately calculated and then added to the original price.

Cost Price

The cost price is the amount paid to purchase an item before any markup. It is the baseline figure used to calculate both profit and selling price.
Understanding the cost price is essential for setting an appropriate selling price and ensuring profitability.

• In our example, the brushes were bought at a cost price of ?8 each.
• This value serves as the starting point in calculating the markup and ultimately the final selling price.

Without knowing the cost price, a business could risk setting prices too low to cover expenses or too high, driving customers away. It ensures that any added markup contributes positively to profit margins.

Selling Price

The selling price is the final price at which an item is sold to the customer. It includes both the cost price and any markup, ensuring that the store earns a profit.
The selling price can be calculated by adding the markup amount to the cost price.
For the paintbrushes, if the cost price is ?8 and the markup amount is calculated at ?1.2:

• Then, the selling price is computed as:

\[\text{Selling Price} = \text{Cost Price} + \text{Markup} = 8 + 1.2 = 9.2\]The selling price is important because it must be competitive enough to attract customers but also sufficient to cover costs and return a profit.