Problem 45 - Algebra A Combined Function

Question

A gasoline station recently increased the price of one grade of gasoline by \(5 \% .\) If this gasoline originally cost \(\$ 2.20\) per gallon, find the mark-up and the new price.

Step-by-Step Solution

Answer

The mark-up is $0.11, and the new price is $2.31.

Step 1: Calculating the Mark-up

The mark-up is the amount added to the original price to get the new price. Since the gasoline was increased by 5%, we calculate 5% of the original price, which is $2.20. We use the formula for percentage increase: \(( ext{Percentage}) \times ( ext{Original Price})\). Therefore, the mark-up is \(0.05 \times 2.20 = 0.11\).

Step 2: Calculating the New Price

To find the new price, we add the mark-up to the original price. We calculated the mark-up as \(0.11 in Step 1. So, the new price is \(2.20 + 0.11 = 2.31\). Thus, the new price of the gasoline per gallon is \)2.31.

Key Concepts

Markup Calculation

Markup calculation is a common method used to determine how much to add to a product's original cost to arrive at its selling price, especially in business. It represents the percentage by which the original price is increased.To calculate the markup:

• Identify the original cost of the item—in our example, it's \(2.20 per gallon.
• Determine the percentage increase. Here, it is given as 5%.
• Apply the formula \( \text{Markup} = \text{Percentage Increase} \times \text{Original Price} \).

For the gasoline, the markup is calculated as:\[ 0.05 \times 2.20 = 0.11 \]This indicates that \)0.11, or 11 cents, must be added to each gallon.Markup is essential for businesses to cover costs and ensure profit. It helps in setting an appropriate selling price while taking into account other expenses that might not be directly included in the original cost.

Price Increase

Price increase refers to the addition to a product's cost over time. It can be due to various factors such as inflation, increased demand, or supply shortages. In our scenario, the price increase comes from a 5% markup.To find the new price after the increase, you use the formula:

• New Price = Original Price + Markup

Given:- Original Price = \(2.20- Markup = \)0.11 as calculatedThe new price is:\[ 2.20 + 0.11 = 2.31 \]Thus, the cost per gallon after the price increase is $2.31.Understanding price increases is essential for consumers and businesses alike, as it factors into budgeting, planning, and financial forecasting.

Mathematical Operations

Mathematical operations are the building blocks for solving percentage-related problems. These operations include multiplication, division, addition, and subtraction. Here, we mainly interact with multiplication and addition.For percentage increase problems:

• Multiply to find the amount represented by the percentage. For instance, to find 5% of $2.20, calculate \(0.05 \times 2.20\).
• Add the percentage amount to the original price. This operation gives the final increased price: \(2.20 + 0.11\).

These simple steps illustrate how mathematical operations can transform given values into useful outcomes. Mastery of these concepts is crucial for solving a variety of practical numerical problems effectively.