If the sum of two numbers is 50 and their ratio is 2:3, what are the numbers?

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Question: If the sum of two numbers is 50 and their ratio is 2:3, what are the numbers?

Options:

Correct Answer: 20 and 30

Solution:

Let the numbers be 2x and 3x. Then, 2x + 3x = 50, 5x = 50, x = 10. The numbers are 20 and 30.

If the sum of two numbers is 50 and their ratio is 2:3, what are the numbers?

If the sum of two numbers is 50 and their ratio is 2:3, what are the numbers?

Step 1: Understand that we have two numbers whose sum is 50.
Step 2: The ratio of the two numbers is given as 2:3.
Step 3: We can represent the two numbers using a variable. Let the first number be 2x and the second number be 3x.
Step 4: Write an equation for their sum: 2x + 3x = 50.
Step 5: Combine like terms in the equation: 5x = 50.
Step 6: Solve for x by dividing both sides of the equation by 5: x = 10.
Step 7: Now, substitute x back into the expressions for the numbers: First number = 2x = 2(10) = 20, Second number = 3x = 3(10) = 30.
Step 8: Therefore, the two numbers are 20 and 30.

Algebraic Equations – The question tests the ability to set up and solve equations based on given conditions (sum and ratio).
Ratios – Understanding and applying the concept of ratios to express relationships between two quantities.