How much does 3.75 kg of chocolate if 0.7 kg cost $4.20
The Correct Answer and Explanation is:
To find the cost of 3.75 kg of chocolate if 0.7 kg costs $4.20, we first determine the cost per kilogram, then multiply that by 3.75 kg.
Step 1: Find the cost per kilogram
We are told that 0.7 kg costs $4.20.
To find the cost of 1 kg, divide $4.20 by 0.7:Cost per kg=4.200.7=6.00\text{Cost per kg} = \frac{4.20}{0.7} = 6.00Cost per kg=0.74.20=6.00
So, the cost of 1 kilogram of chocolate is $6.00.
Step 2: Multiply by 3.75 kg
Now, multiply the unit price by the total weight:Cost of 3.75 kg=3.75×6.00=22.50\text{Cost of 3.75 kg} = 3.75 \times 6.00 = 22.50Cost of 3.75 kg=3.75×6.00=22.50
Answer: The cost of 3.75 kg of chocolate is $22.50
Explanation (300 words):
To solve this type of problem, it is helpful to break it down into smaller steps. First, identify what information is given and what you need to find. In this case, you are given the cost of a smaller quantity of chocolate and asked to determine the cost for a larger amount.
This is a proportional relationship. If 0.7 kg costs $4.20, then 1 kg will cost more because it is a larger quantity. To find the price per kilogram, you divide the given price by the weight. Dividing $4.20 by 0.7 kg tells you how much one kilogram costs, which is $6.00. This is the unit rate.
Once the unit rate is known, you can multiply it by the number of kilograms you want to buy. Since you are interested in buying 3.75 kg, you multiply 3.75 by $6.00. This gives a total of $22.50.
This method is commonly used in everyday shopping, especially when dealing with bulk items. Understanding unit price helps compare prices and make better buying decisions. It is also a key part of ratio and proportion skills in mathematics, helping to solve problems involving comparisons and scaling.
