Question

Nick needs to order 500 pens from his supplier. The catalog shows that these pens come in cases of 24 boxes with 10 pens in each box. Nick knows that he may NOT order partial cases. What is the fewest number of cases he should order? A. 2 B. 3 C. 18 D. 21 E. 50

Short answer

Answer: B. 3

Step-by-step solution

Calculate the number of pens in one case

First, let's calculate how many pens are in one case. There are 24 boxes in a case and each box has 10 pens. So the number of pens in one case is: 24 boxes × 10 pens/box = 240 pens/case

Calculate the minimum cases needed

Now that we know there are 240 pens in a case, we'll divide 500 pens by 240 pens/case to find how many cases he should order: 500 pens ÷ 240 pens/case ≈ 2.083 cases

Round up to the next whole number

Since Nick cannot order partial cases, we need to round 2.083 up to the next whole number. This gives us: 3 cases

Choose the correct answer

As 3 cases are needed to fill the 500 pens, the correct answer is: B. 3

Key concepts

Mathematical Problem-Solving

Mathematical problem-solving is one of the vital skills learned in school and is essential in our everyday lives. In the provided exercise, Nick's challenge of ordering pens requires an effective strategy to solve the problem.

Initially, to approach a mathematical problem, one should understand the question, identify the relevant information, and devise a plan. For Nick, the challenge was to find out the minimum number of cases he needs without ordering partial cases. Understanding that each case has a fixed quantity allowed him to stipulate a multiplication problem to find out the total number of pens per case. In practical terms, once you have recognized the type of problem, the steps to solve it become clearer, which in Nick's case involved basic arithmetic and rounding up to the nearest whole number.

Critical thinking comes into play by interpreting the results. For Nick, although the calculation yielded a decimal, he interpreted that as needing to order full cases, thus rounding up. It is crucial to not just perform calculations but to understand the real-world implications of your result. Nick's scenario serves as an excellent example of the necessity to not just solve for a number but to apply logical reasoning to arrive at a practical solution.

Rounding and Estimation

Rounding and estimation are powerful mathematical tools used to simplify numbers to make them easier to work with. In our example problem, after calculating the number of cases needed, Nick got an answer of approximately 2.083. Since ordering a fraction of a case isn't practical, rounding was necessary.

Rounding is the process of replacing a number with another number that is approximately equal but simpler. Here, we use rounding up, which means going to the next highest whole number if the part we are dropping is greater than or equal to 0.5. Since Nick got 2.083, he had to round up to 3 cases to ensure he had enough pens.

Rounding not only affects mathematical calculations but also influences everyday decisions like budgeting, time management, and purchasing. By rounding up, Nick ensures he meets his needs without falling short. Additionally, it demonstrates an estimation skill - knowing when to round up or down can indicate an understanding of the context and the consequences of the estimate made.

Basic Arithmetic

Basic arithmetic is the foundation of all mathematics. This includes operations such as addition, subtraction, multiplication, and division - the kind of math we use daily. In the textbook question about ordering pens, Nick utilized multiplication to calculate the total number of pens in a case, and division to ascertain how many cases he would need for 500 pens.

The simplicity of arithmetic hides its power; it enables us to solve a variety of practical problems. Whether it's budgeting your expenses, calculating time, or, like Nick, ordering enough product, proficiency in these operations is essential. The key is to perform these calculations methodically: multiplication first to find out the quantity per case, then division to relate that to the quantity needed. Sometimes, the solution isn't a whole number, as Nick found out. That's when we apply additional arithmetic principles, like rounding, to find the most practical answer.

In practice, when numbers become large or complex, understanding the properties of numbers and operations becomes even more necessary to perform calculations effectively and efficiently. Nick's problem is an illustration of using basic arithmetic to solve real-world scenarios confidently and competently.