Class Five and six are to share: $2^{150}$. Find the numbers in the ratio of $1:2$. Find the number of theirs.
Answer (1)
Let x be the number of items in Class Five, then the number of items in Class Six is 2 x .
The total number of items is x + 2 x = 3 x , which is equal to 2 150 .
Solve for x : 3 x = 2 150 ⟹ x = 3 2 150 .
The number of items in Class Five is 3 2 150 and the number of items in Class Six is 3 2 151 . 3 2 150 , 3 2 151
Explanation
Problem Analysis We are given that the total number of items is 2 150 and that they are divided into two classes, Five and Six, in the ratio 1 : 2 . Our goal is to find the number of items in each class.
Setting up the Equation Let x be the number of items in Class Five and 2 x be the number of items in Class Six. Then the total number of items is x + 2 x = 3 x . We are given that the total number of items is 2 150 , so we have the equation 3 x = 2 150 .
Solving for x To solve for x , we divide both sides of the equation by 3: x = 3 2 150 This is the number of items in Class Five.
Calculating the Number of Items in Class Six The number of items in Class Six is 2 x , so we have: 2 x = 2 ⋅ 3 2 150 = 3 2 151 This is the number of items in Class Six.
Final Answer Therefore, the number of items in Class Five is 3 2 150 and the number of items in Class Six is 3 2 151 .
Examples
Imagine you are distributing tasks in a project where the workload needs to be divided in a 1:2 ratio between two teams. If the total 'workload' is represented by 2 150 units, this problem helps you determine how many units of work each team should handle to maintain the desired ratio. This ensures fair and balanced contribution from both teams, optimizing project efficiency and team satisfaction.
