If the ratio of the ages of A and B is 3:4 and the sum of their ages is 28, what

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Question: If the ratio of the ages of A and B is 3:4 and the sum of their ages is 28, what is A\'s age? (2022)

Options:

Correct Answer: 12

Exam Year: 2022

Solution:

Let A\'s age be 3x and B\'s age be 4x. Then, 3x + 4x = 28, so 7x = 28, giving x = 4. Thus, A\'s age = 3x = 12.

If the ratio of the ages of A and B is 3:4 and the sum of their ages is 28, what is A's age? (2022)

If the ratio of the ages of A and B is 3:4 and the sum of their ages is 28, what is A's age? (2022)

Step 1: Understand the ratio of ages. A's age is represented as 3x and B's age as 4x.
Step 2: Write the equation for the sum of their ages. Since the sum is 28, we write 3x + 4x = 28.
Step 3: Combine the terms on the left side of the equation. This gives us 7x = 28.
Step 4: Solve for x by dividing both sides of the equation by 7. This gives us x = 4.
Step 5: Find A's age by substituting x back into the expression for A's age. A's age = 3x = 3 * 4 = 12.

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