Divide 54 oranges in the ratio of $4:2$ between Teekay and Lute.
Answer (1)
Represent Teekay's share as 4 x and Lute's share as 2 x .
Set up the equation 4 x + 2 x = 54 to represent the total number of oranges.
Solve for x : 6 x = 54 , so x = 9 .
Calculate Teekay's share: 4 × 9 = 36 , and Lute's share: 2 × 9 = 18 . The final answer is 36 oranges for Teekay and 18 oranges for Lute .
Explanation
Understanding the Problem We need to divide 54 oranges between Teekay and Lute in the ratio of 4:2. This means that for every 4 parts Teekay gets, Lute gets 2 parts.
Setting up the Equation Let's represent Teekay's share as 4 x and Lute's share as 2 x , where x is a common factor. The total number of oranges is the sum of their shares, so we have the equation: 4 x + 2 x = 54
Simplifying the Equation Combining the terms on the left side, we get: 6 x = 54
Solving for x Now, we solve for x by dividing both sides of the equation by 6: x = 6 54 = 9
Calculating the Shares Now that we have the value of x , we can find the number of oranges each person gets. Teekay's share is: 4 x = 4 × 9 = 36 Lute's share is: 2 x = 2 × 9 = 18
Final Answer Therefore, Teekay gets 36 oranges and Lute gets 18 oranges.
Examples
Ratios are commonly used in everyday life. For example, when baking, you might need to mix flour and sugar in a specific ratio, like 3:1. If you're making a larger batch and need to use a total of 4 cups, you'd divide the total amount according to the ratio. Similarly, in business, profits or losses are often shared among partners based on a pre-agreed ratio. Understanding how to divide quantities in a given ratio helps ensure fairness and consistency in various real-world scenarios.
