Question

Company A sells 60 pens for \(\$ 15.00\) , while Company B sells the same type of pens 40 for \(\$ 8.00\) . Which company's price per pen is cheaper, and what is that price? A. Company A, at \(\$ 0.20\) B. Company A, at \(\$ 0.23\) C. Company A, at \(\$ 0.25\) D. Company B, at \(\$ 0.20\) E. Company B, at \(\$ 0.25\)

Short answer

Answer: D. Company B, at $0.20 per pen.

Step-by-step solution

Calculate Company A's Price per Pen

To find the price per pen for Company A, divide the total price of their pens (\(\$15.00\)) by the number of pens they sell (60). Price per pen for Company A = \(\frac{\$15.00}{60}\)

Calculate Company B's Price per Pen

To find the price per pen for Company B, divide the total price of their pens (\(\$8.00\)) by the number of pens they sell (40). Price per pen for Company B = \(\frac{\$8.00}{40}\)

Compare Both Companies' Prices per Pen

Now that we have the prices per pen for both companies, compare them to determine which company offers the lower price per pen.

Find the Cheaper Option

Based on the calculations from Steps 1 and 2, determine which company has the lowest price per pen, and match that price to one of the answer choices provided. Price per pen for Company A = \(\frac{\$15.00}{60}\) = \(\$ 0.25\) Price per pen for Company B = \(\frac{\$8.00}{40}\) = \(\$ 0.20\) Company B has the lower price per pen. The correct answer is: D. Company B, at \(\$ 0.20\)

Key concepts

Math Word Problems

When students encounter math word problems, it can sometimes feel like a puzzle. These types of questions require one to read a scenario and extract the necessary information to form equations. A common real-life example is determining the best price per unit when shopping, like comparing prices of pens between two companies. Here are some strategies to solve math word problems:

• Read the problem carefully and identify what you are being asked to find.
• Identify and organize the relevant information given in the problem.
• Translate the words into numbers and symbols to form an equation or a set of equations.
• Solve the equation(s) using basic arithmetic.
• Check your answer to make sure it makes sense in the context of the problem.

To make the process less intimidating, simplifying the problem into a series of smaller, manageable steps can greatly increase the chance of solving it correctly—much like the step-by-step solution provided to the pen pricing problem.

Basic Arithmetic

The foundation of solving math word problems is a strong grasp of basic arithmetic—addition, subtraction, multiplication, and division. These fundamental operations are the tools needed to dissect and solve a variety of mathematical puzzles. For example, to find out which company offers a better price for their pens, you divide the total price by the number of units (pens) to find out the price per pen. This process is called unit price calculation. It's expressed as:

Price Per Unit Formula

Price Per Unit = \frac{Total Price}{Number of Units}

By applying basic division, you can find out that Company A offers pens at \(\$0.25\) each, while Company B offers them at \(\$0.20\) each.

Remember, these operations aren't just for classroom exercises—they're skills you'll use in many aspects of life, such as budgeting or shopping. In instances like these, opting for rounded numbers can sometimes make mental calculations easier and quicker, especially during exams or real-life situations.

ACT Prep

The ACT is a standardized test used for college admissions that includes a math section designed to measure students' mathematical skills and reasoning abilities. Problems similar to the price per pen comparison are typical for the ACT, as it assesses a range of competencies including basic operations, algebra, geometry, and critical thinking within time constraints.

Efficient ACT preparation involves practice with real-world scenarios like the exercise provided. It is essential to:

• Familiarize yourself with the format of the questions.
• Practice under timed conditions to improve speed and accuracy.
• Develop strategies for different types of questions.
• Frequent review of basic arithmetic to ensure a strong foundation.

By practicing these types of exercises, students enhance their problem-solving skills and learn to quickly determine the best strategy to arrive at the correct answer. Making connections to real-life situations as seen in this price per unit problem can also make the task less abstract and more relatable, aiding in retention and recall during the test.