The difference between the ages of two siblings is 7 years. If the sum of their ages is 21 years, how old is t

Question

The difference between the ages of two siblings is 7 years. If the sum of their ages is 21 years, how old is the elder of the siblings?

Examoogle · Accepted Answer

The correct answer is Option D: 14 years. For two values with given sum $S$ and difference $D$, the larger value is always $(S+D)/2$ and the smaller is $(S-D)/2$.

Step-by-Step Solution & Concepts:
Shortcut Trick: For two values with given sum $S$ and difference $D$, the larger value is always $(S+D)/2$ and the smaller is $(S-D)/2$.

Formula Used: $$x + y = 21$$, $$x - y = 7$$

Given: Difference between ages = 7 years, Sum of ages = 21 years.

Steps: Define variables: Let the age of the elder sibling be $x$ and the younger sibling be $y$. We are given two equations based on the problem statement.. Solve the system of equations: Add the two equations to eliminate $y$ and solve for $x$: $(x + y) + (x - y) = 21 + 7$, which simplifies to $2x = 28$.. Calculate the final age: Divide by 2 to find the age of the elder sibling $x$.

Answer: D is correct because the elder sibling is 14 years old, derived from $(21+7)/2 = 14$.

Exam Tip: This concept of finding two numbers given their sum and difference is fundamental in solving ratio and proportion problems and speed/distance problems involving upstream/downstream motion.

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)