Class five cine seats are to share 150. They are in the ratio of 2 to [tex]$2^2$[/tex]. Find the number in them.
Answer (1)
Represent the number of items in the two classes as 2 x and 4 x .
Set up the equation 2 x + 4 x = 150 to represent the total number of items.
Solve for x : x = 6 150 = 25 .
Calculate the number of items in each class: 2 x = 50 and 4 x = 100 . The number of items in themis is 50 , 100 .
Explanation
Understanding the Problem We are given that there are 150 items in total, divided into two classes. The ratio of the number of items in the two classes is 2 to 2 2 , which simplifies to 2 to 4. Our goal is to find the number of items in each class.
Setting up the Equation Let's denote the number of items in the first class as 2 x and the number of items in the second class as 4 x , where x is a common ratio. The total number of items is the sum of the items in both classes, so we have the equation: 2 x + 4 x = 150
Simplifying the Equation Combining the terms on the left side of the equation, we get: 6 x = 150
Solving for x Now, we solve for x by dividing both sides of the equation by 6: x = 6 150 = 25
Finding the Number of Items in Each Class Now that we have the value of x , we can find the number of items in each class. The number of items in the first class is: 2 x = 2 × 25 = 50 The number of items in the second class is: 4 x = 4 × 25 = 100
Final Answer Therefore, there are 50 items in the first class and 100 items in the second class.
Examples
Imagine you're dividing tasks between two teams with a specific ratio in mind. If you have 150 tasks and want to split them between a smaller team and a larger team in a 2:4 ratio, this problem helps you determine how many tasks each team should handle. The smaller team would get 50 tasks, and the larger team would get 100 tasks, ensuring a balanced workload distribution based on the team sizes. This kind of proportional division is useful in resource allocation, project management, and many other real-world scenarios.
