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Chapter 1: Problem 40

The H. J. Heinz Company ships 16-oz bottles of ketchup in cartons containing 12 bottles each. How many cartons are needed to ship 528 bottles of ketchup?

Short Answer

Expert verified
44 cartons

Step by step solution

01

- Understand the given information

There are cartons which each contain 12 bottles of ketchup. Our goal is to determine how many cartons are needed to ship a total of 528 bottles.
02

- Set up the equation

We need to divide the total number of bottles by the number of bottles each carton can hold. This can be set up as follows: \[ \text{Number of cartons} = \frac{\text{Total bottles}}{\text{Bottles per carton}} \] Here, Total bottles = 528 and Bottles per carton = 12.
03

- Perform the division

Calculate the number of cartons by dividing 528 by 12. \[ \text{Number of cartons} = \frac{528}{12} = 44 \]
04

- Interpret the result

The result from the division gives us the number of cartons needed. So, 44 cartons are required to ship 528 bottles of ketchup.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

multiplication and division
Understanding the relationship between multiplication and division is crucial for solving problems efficiently. Division can be seen as the inverse operation of multiplication. This means if multiplication combines groups of items together, division splits them into equal parts.
For example, if you know that each carton contains 12 bottles of ketchup, and you need to ship 528 bottles, division helps you determine the number of cartons required.
Mathematically, you express this as: \[\frac{528}{12} = 44\]
This equation tells us that 528 bottles divided into groups of 12 bottles each results in 44 groups, or cartons.
real-life math applications
Mathematics isn't just about solving abstract problems; it has practical applications in our everyday lives. One key area is logistics and packaging, which are essential for businesses.
For instance, in the given exercise, calculating how many cartons are needed to ship a certain number of bottles is a real-life task. Companies routinely perform such calculations to ensure efficient product distribution.
By understanding this process, you can appreciate how math helps businesses reduce costs and streamline operations. Knowing the number of cartons needed prevents over- or under-shipment, ensuring that products reach their destinations properly packed.
word problems in mathematics
Word problems often require translating a real-world scenario into a mathematical model, making problem-solving an essential skill. In our example, understanding that each carton holds 12 bottles and that you need to find out how many cartons are needed for 528 bottles is the first step.
Breaking it down:
  • Read the problem carefully to determine what's given and what's required.
  • Set up the appropriate equation with the given numbers. Here, it's \(\frac{528}{12}\).
  • Perform the arithmetic operation, which in this case is division.
  • Finally, interpret the result in the context of the problem.
This structured approach ensures you address every part of the problem methodically, leading to the correct solution.

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Most popular questions from this chapter

Write exponential notation. $$ 3 \cdot 3 \cdot 3 \cdot 3 $$

Solve by trial. $$ y \cdot 17=0 $$

Simplify. $$ (2+5)^{2} $$

Solve. Be sure to check. $$ 10,534 \div 458=q $$

Evaluate. $$ 7^{2} $$
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