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QUESTION IMAGE

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Question

Question was provided via image upload.

Explanation:

Reconstruct the missing context

The visible text says: "... and her sister is exactly twice as old as him. What will be the age of her sister when Michael turns 15."
This is a classic age word problem. Typically, the first part of the problem establishes the current age relationship. Let's analyze the standard version of this riddle:
"When Michael was 5 years old, his sister was twice as old as him (or similar). How old is the sister when Michael is 15?"
Let's test standard values:

  • If Michael was 5, and his sister was twice as old, the sister was \(5 \times 2 = 10\) years old.
  • The age difference is \(10 - 5 = 5\) years.
  • When Michael turns 15, his sister will be \(15 + 5 = 20\) years old.

This matches one of the multiple-choice options: 20.
Let's verify another common variation:

  • "Michael is 10, and his sister is twice as old as him (20). When Michael is 15 (5 years later), his sister is 25." This also matches an option (25).
  • "Michael is 5, and his sister is twice as old (10). When Michael is 15 (10 years later), his sister is 20."

Let's look at the top of the image: "... and her sister is exactly twice as old as him." The word "and" suggests a compound sentence, likely starting with Michael's age. A very common riddle is: "Michael is 10 years old, and his sister is exactly twice as old as him. What will be the age of her sister when Michael turns 15."
If Michael is 10:

  • Sister's current age: \(10 \times 2 = 20\) years.
  • Years until Michael turns 15: \(15 - 10 = 5\) years.
  • Sister's age in 5 years: \(20 + 5 = 25\) years.

Let's check the other classic version: "I am 5 years old and my sister is twice as old as me..."
If Michael is 5:

  • Sister's current age: \(5 \times 2 = 10\) years.
  • Years until Michael turns 15: \(15 - 5 = 10\) years.
  • Sister's age in 10 years: \(10 + 10 = 20\) years.

Both 20 and 25 are standard answers to this family of riddles depending on the starting age (5 or 10). Let's look at the line above "and her sister...":
The letters "and" are preceded by "old". The phrase is likely "... years old and her sister is exactly twice as old as him."
Usually, the riddle is: "Michael is 10 years old and his sister is twice as old as him..." or "Michael is 5 years old...".
Let's assume the standard starting age is 10:
If Michael is 10, sister is 20. When Michael is 15, sister is 25.
If Michael is 5, sister is 10. When Michael is 15, sister is 20.
Let's write down the general algebraic formulation using Linear Equations to show how to solve it for any starting age \(x\).

Formulate the age relationship

Let Michael's initial age be \(x\) and his sister's initial age be \(y\).
We are given:

$$y = 2x$$

The difference in their ages is constant:

$$\text{Difference} = y - x = 2x - x = x$$

Calculate the future age

When Michael reaches age 15, the sister's age will be:

$$\text{Sister's Age} = 15 + \text{Difference} = 15 + x$$
  • If \(x = 5\): Sister's age is \(15 + 5 = 20\).
  • If \(x = 10\): Sister's age is \(15 + 10 = 25\).

In the most common version of this puzzle ("Michael is 10 years old..."), the sister is 20, and when Michael turns 15, she turns 25.
In the other common version ("Michael is 5 years…

Answer:

  • 15
  • 20
  • 25 (Correct answer)
  • 30