If the ratio of the ages of A and B is 3:4 and the sum of their ages is 56 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 56 years, what is A\'s age?

Options:

Correct Answer: 24

Solution:

Let A\'s age be 3x and B\'s age be 4x. Then, 3x + 4x = 56, giving 7x = 56, so x = 8. Thus, A\'s age = 3x = 24.

If the ratio of the ages of A and B is 3:4 and the sum of their ages is 56 years, what is A's age?

If the ratio of the ages of A and B is 3:4 and the sum of their ages is 56 years, what is A's age?

Step 1: Understand the ratio of ages. A's age is represented as 3 parts and B's age as 4 parts.
Step 2: Let 'x' be a common multiplier. So, A's age can be written as 3x and B's age as 4x.
Step 3: Write the equation for the sum of their ages. The equation is 3x + 4x = 56.
Step 4: Combine the terms on the left side of the equation. This gives us 7x = 56.
Step 5: Solve for 'x' by dividing both sides of the equation by 7. This gives us x = 8.
Step 6: Now, find A's age by substituting 'x' back into the expression for A's age. A's age = 3x = 3 * 8.
Step 7: Calculate 3 * 8, which equals 24. Therefore, A's age is 24 years.

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.
Age Problems – Applying mathematical reasoning to solve problems related to the ages of individuals.