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

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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 years, what is A\'s age? (2021)

Options:

Correct Answer: 14

Exam Year: 2021

Solution:

Let A\'s age be 3x and B\'s age be 4x. Then, 3x + 4x = 28, giving 7x = 28, so 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 years, what is A's age? (2021)

If the ratio of the ages of A and B is 3:4 and the sum of their ages is 28 years, what is A's age? (2021)

Step 1: Understand that the ratio of A's age to B's age is 3:4. This means for every 3 parts of A's age, B has 4 parts.
Step 2: Let A's age be represented as 3x and B's age as 4x, where x is a common multiplier.
Step 3: Write the equation for the sum of their ages: 3x + 4x = 28.
Step 4: Combine the terms on the left side: 7x = 28.
Step 5: Solve for x by dividing both sides by 7: x = 28 / 7, which gives x = 4.
Step 6: Now, find A's age by substituting x back into the equation 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 algebra.
Algebraic Equations – Setting up and solving linear equations based on given conditions.