If the ratio of the ages of A and B is 5:3 and the sum of their ages is 64 years

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Question: If the ratio of the ages of A and B is 5:3 and the sum of their ages is 64 years, what is A\'s age?

Options:

Correct Answer: 40

Solution:

Let A\'s age be 5x and B\'s age be 3x. Then, 5x + 3x = 64, which gives 8x = 64. Therefore, x = 8, and A\'s age is 5x = 40 years.

If the ratio of the ages of A and B is 5:3 and the sum of their ages is 64 years, what is A's age?

If the ratio of the ages of A and B is 5:3 and the sum of their ages is 64 years, what is A's age?

Step 1: Understand the ratio of ages. A's age is represented as 5x and B's age as 3x.
Step 2: Write the equation for the sum of their ages. The equation is 5x + 3x = 64.
Step 3: Combine the terms on the left side of the equation. This gives us 8x = 64.
Step 4: Solve for x by dividing both sides of the equation by 8. This gives us x = 8.
Step 5: Find A's age by substituting x back into the expression for A's age. A's age is 5x, which is 5 * 8 = 40 years.

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