If the ratio of the ages of A and B is 3:4 and the sum of their ages is 70 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 70 years, what is A\'s age?

Options:

Correct Answer: 35 years

Solution:

Let A\'s age be 3x and B\'s age be 4x. Then, 3x + 4x = 70, so 7x = 70, giving x = 10. A\'s age = 3x = 30 years.

If the ratio of the ages of A and B is 3:4 and the sum of their ages is 70 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 70 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 = 70.
Step 4: Combine the terms on the left side of the equation. This gives us 7x = 70.
Step 5: Solve for 'x' by dividing both sides of the equation by 7. This gives us x = 10.
Step 6: Now, find A's age by substituting 'x' back into the expression for A's age. A's age = 3x = 3 * 10.
Step 7: Calculate A's age. A's age = 30 years.

Ratio and Proportion – Understanding how to express relationships between quantities using ratios.
Algebraic Equations – Setting up and solving equations based on given relationships and conditions.
Age Problems – Applying mathematical reasoning to solve problems related to the ages of individuals.