The ages of two siblings are in the ratio 4:5. If the sum of their ages is 72, w

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Question: The ages of two siblings are in the ratio 4:5. If the sum of their ages is 72, what is the age of the older sibling? (2023)

Options:

Correct Answer: 40

Exam Year: 2023

Solution:

Let the ages be 4x and 5x. Then, 4x + 5x = 72, leading to 9x = 72, so x = 8. The older sibling\'s age is 5x = 40.

The ages of two siblings are in the ratio 4:5. If the sum of their ages is 72, what is the age of the older sibling? (2023)

The ages of two siblings are in the ratio 4:5. If the sum of their ages is 72, what is the age of the older sibling? (2023)

Step 1: Understand that the ages of the two siblings are in a ratio of 4:5. This means if one sibling's age is 4 parts, the other sibling's age is 5 parts.
Step 2: Let the age of the first sibling be 4x and the age of the second sibling be 5x, where x is a common multiplier.
Step 3: Write an equation for the sum of their ages: 4x + 5x = 72.
Step 4: Combine the terms on the left side of the equation: 9x = 72.
Step 5: Solve for x by dividing both sides of the equation by 9: x = 72 / 9.
Step 6: Calculate the value of x: x = 8.
Step 7: Find the age of the older sibling by calculating 5x: 5 * 8 = 40.
Step 8: Conclude that the age of the older sibling is 40.

Ratios – Understanding and applying ratios to represent relationships between quantities.
Algebraic Equations – Setting up and solving equations based on given conditions.
Word Problems – Translating a real-world scenario into a mathematical problem.