If the ratio of the ages of A and B is 3:4 and the sum of their ages is 70, 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 70, what is A\'s age? (2022)

Options:

Correct Answer: 35

Exam Year: 2022

Solution:

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

If the ratio of the ages of A and B is 3:4 and the sum of their ages is 70, 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 70, what is A's age? (2022)

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 = 70.
Step 4: Combine the terms on the left side: 3x + 4x equals 7x, so we have 7x = 70.
Step 5: Solve for x by dividing both sides of the equation by 7: x = 70 / 7, which gives 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 = 30.

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 conditions.