Question

A fish company delivers \(22 \mathrm{~kg}\) of salmon, \(5.5 \mathrm{~kg}\) of crab, and \(3.48 \mathrm{~kg}\) of oysters to your seafood restaurant. a. What is the total mass, in kilograms, of the seafood? b. What is the total number of pounds?

Short answer

Total mass: 30.98 kg or 68.29 pounds

Step-by-step solution

- Calculate the Total Mass in Kilograms

To find the total mass, add the masses of the salmon, crab, and oysters. The equation is:\[ 22 + 5.5 + 3.48 \]

- Perform the Addition

First, add 22 (salmon) and 5.5 (crab): \[ 22 + 5.5 = 27.5 \] Then, add the result to 3.48 (oysters): \[ 27.5 + 3.48 = 30.98 \] Therefore, the total mass is 30.98 kg.

- Convert Kilograms to Pounds

Use the conversion factor: 1 kg = 2.20462 pounds. Multiply the total mass in kilograms by this factor: \[ 30.98 \times 2.20462 \]

- Perform the Multiplication

Calculate the product: \[ 30.98 \times 2.20462 = 68.286 \] Therefore, the total mass in pounds is approximately 68.29 pounds.

Key concepts

unit conversion

Unit conversion is a fundamental concept in mathematics and science. It involves changing a quantity expressed in one unit to another unit.
For example, converting kilograms to pounds or meters to feet.
Conversions are essential because different regions or fields may use different units for the same quantity.
To convert between units: Use conversion factors.

• A conversion factor is a ratio that expresses how many of one unit equals another.
• For example, the conversion factor between kilograms and pounds is 1 kg = 2.20462 pounds.

In practical scenarios, unit conversions ensure consistency and understanding across different measurement systems.

addition of masses

Addition of masses means summing the weights of multiple objects to get a total weight.
It's a basic arithmetic operation used in many real-life applications.
For instance, in the exercise, we add the masses of salmon, crab, and oysters.

• First, add the mass of salmon (22 kg) and crab (5.5 kg).
• This gives 27.5 kg.
• Next, add this sum to the mass of the oysters (3.48 kg).
• Thus, we get 27.5 + 3.48 = 30.98 kg.

The total mass, 30.98 kg, represents all the seafood the company delivers.

kilograms to pounds conversion

Converting between kilograms and pounds is common in daily life, especially in countries using different measurement systems.
To convert kilograms to pounds, multiply by the conversion factor 2.20462.

• For instance, to convert 30.98 kg to pounds: 30.98 * 2.20462.
• This calculation gives about 68.29 pounds.

The conversion factor ensures precision in the conversion.
Remember, rounding the result is often useful for simplicity, like approximating 68.286 to 68.29 pounds in the exercise.

arithmetic operations

Arithmetic operations include addition, subtraction, multiplication, and division.
These operations are key to solving many mathematical problems.
In the exercise:

• We use addition to find the total mass of the seafood.
• We perform multiplication to convert kilograms to pounds.

It's crucial to understand the order of operations:

• First, perform any calculations inside brackets.
• Next, handle multiplication and division from left to right.
• Finally, address addition and subtraction from left to right.

Grasping these basic operations makes tackling more complex problems much easier.