The ages of O and P are in the ratio 5:3. If the sum of their ages is 64, what i

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Question: The ages of O and P are in the ratio 5:3. If the sum of their ages is 64, what is O\'s age?

Options:

Correct Answer: 40

Solution:

Let O\'s age be 5x and P\'s age be 3x. Then, 5x + 3x = 64. Solving gives x = 8, O\'s age = 5 * 8 = 40.

The ages of O and P are in the ratio 5:3. If the sum of their ages is 64, what is O's age?

The ages of O and P are in the ratio 5:3. If the sum of their ages is 64, what is O's age?

Step 1: Understand that the ages of O and P are in a ratio of 5:3. This means for every 5 parts O has, P has 3 parts.
Step 2: Let O's age be represented as 5x and P's age as 3x, where x is a common multiplier.
Step 3: Write an equation for the sum of their ages: 5x + 3x = 64.
Step 4: Combine the terms on the left side of the equation: 8x = 64.
Step 5: Solve for x by dividing both sides of the equation by 8: x = 64 / 8 = 8.
Step 6: Now, find O's age by substituting x back into the expression for O's age: O's age = 5 * x = 5 * 8 = 40.

Ratios and Proportions – Understanding how to express relationships between quantities using ratios and how to solve for unknowns using algebra.
Algebraic Equations – Setting up and solving linear equations based on given conditions.