Question

The tank currently holds \(5,000\) gallons of milk. Each gallon of milk weighs about 8 pounds. About how many pounds does this milk weigh? F. \(\quad 625\) G. \(4,000\) H. \(4,992\) J. 4008 K. \(40,000\)

Short answer

A) 5,000 B) 12,000 C) 30,000 D) 32,000 E) 40,000 Answer: E) 40,000

Step-by-step solution

Identify the given information

We are given that the tank holds 5,000 gallons of milk and each gallon of milk weighs 8 pounds.

Write down the formula to calculate the total weight

The formula to calculate the total weight of the milk is: Total weight = Number of gallons × Weight of each gallon

Plug in the given values into the formula and calculate the total weight

Total weight = 5,000 gallons × 8 pounds/gallon = 40,000 pounds.

Choose the correct option

Based on our calculation, the total weight of the milk is 40,000 pounds. So, the correct answer is option K, \(40,000\).

Key concepts

Word Problems

Word problems in mathematics often describe realistic situations using numbers and operations to find a solution. They require a student to read and understand the text, identify the relevant information, and then apply mathematical equations to solve the problem.

For example, the problem statement 'The tank currently holds 5,000 gallons of milk. Each gallon of milk weighs about 8 pounds. About how many pounds does this milk weigh?' describes a realistic situation involving milk in a tank. The key steps in solving word problems include:

• Reading the problem carefully
• Identifying the given information (such as the amount of milk and its weight per gallon)
• Understanding the question being asked
• Translating the words into a mathematical formula
• Performing the necessary calculations
• Selecting the answer that corresponds with the calculation

By breaking down the word problem into these manageable steps, the solution becomes more accessible.

Unit Conversion

Unit conversion is a critical skill in mathematics, especially when it comes to solving real-world problems. It involves changing a measurement from one unit to another without changing the quantity. For example, converting inches to feet or gallons to pints.

In our milk problem, however, the conversion is implicit within the multiplication process since we're dealing with gallons of milk being converted into pounds through the given weight per gallon. No additional conversion step is required here, as we're not changing measurement systems or types of measurement units. The importance lies in understanding that the final answer needs to be in pounds, which is a unit of weight, while the initial information is provided in terms of volume (gallons).

Multiplication of Units

Multiplication of units is an essential operation when combining different measurements or units to obtain a new quantity. The process involves multiplying the numerical values and also correctly combining the units.

For example, if one gallon of milk weighs 8 pounds, as in the given problem, you multiply the number of gallons (5,000) by the weight per gallon (8 pounds/gallon). Here's the detailed calculation:
Total weight = Number of gallons × Weight per gallon
= 5,000 gallons × 8 pounds/gallon
= 40,000 pounds

When multiplying units, the gallon units cancel each other out, and we're left with pounds as the unit for the total weight. This concept is vital in understanding problems that involve compound measurements, like converting a volume of liquid into its corresponding weight.