Question
Cleo is 38 years old, which is twice as old as Clara will be in 7 years.
Part A
Which of the following statements about Clara’s age are true?
Select all that apply.
A Clara is 12 years old.
B In 14 years, Clara will be 38.
C Clara is 24 years old.
D In 26 years, Clara will be 38.
E In 26 years, Clara will be 50.
Part B
Which of the following statements about Cleo’s age are true?
Select all that apply.
A When Clara is 38, Cleo will be 57.
B When Clara is 38, Cleo will be 64.
C Cleo is 26 years older than Clara.
D Cleo is 14 years older than Clara.
E When Clara is 20, Cleo will be 46.
Part A
Which of the following statements about Clara’s age are true?
Select all that apply.
A Clara is 12 years old.
B In 14 years, Clara will be 38.
C Clara is 24 years old.
D In 26 years, Clara will be 38.
E In 26 years, Clara will be 50.
Part B
Which of the following statements about Cleo’s age are true?
Select all that apply.
A When Clara is 38, Cleo will be 57.
B When Clara is 38, Cleo will be 64.
C Cleo is 26 years older than Clara.
D Cleo is 14 years older than Clara.
E When Clara is 20, Cleo will be 46.
Answers
GPT-4o mini
To solve the problem, let's start by determining Clara's current age based on the information given.
Cleo is currently 38 years old, and we know that this is twice Clara's age in 7 years. Let's denote Clara's current age as \( C \). In 7 years, Clara's age will be \( C + 7 \). According to the problem, we have:
\[ 38 = 2 \times (C + 7) \]
Now, let's solve for Clara's age, \( C \):
1. \( 38 = 2(C + 7) \)
2. \( 38 = 2C + 14 \)
3. \( 38 - 14 = 2C \)
4. \( 24 = 2C \)
5. \( C = 12 \)
So, Clara is currently 12 years old.
Now we can evaluate the statements for Part A regarding Clara’s age:
A) Clara is 12 years old. **(True)**
B) In 14 years, Clara will be 38. \( 12 + 14 = 26 \) **(False)**
C) Clara is 24 years old. **(False)**
D) In 26 years, Clara will be 38. \( 12 + 26 = 38 \) **(True)**
E) In 26 years, Clara will be 50. \( 12 + 26 = 38 \) **(False)**
So, for Part A, the true statements about Clara's age are:
- A (True)
- D (True)
Now let's evaluate Part B concerning Cleo's age:
Cleo is currently 38 years old, and we have established Clara is currently 12 years old.
Now we'll evaluate the statements for Part B:
A) When Clara is 38, Cleo will be 57. \( 38 - 12 = 26 \) years from now; thus, Cleo will be \( 38 + 26 = 64 \). **(False)**
B) When Clara is 38, Cleo will be 64. **(True)**
C) Cleo is 26 years older than Clara. \( 38 - 12 = 26 \). **(True)**
D) Cleo is 14 years older than Clara. **(False)**
E) When Clara is 20, Cleo will be 46. \( 20 - 12 = 8 \), \( 38 + 8 = 46 \). **(True)**
So, for Part B, the true statements about Cleo's age are:
- B (True)
- C (True)
- E (True)
### Summary:
**Part A True Statements**: A, D
**Part B True Statements**: B, C, E
Cleo is currently 38 years old, and we know that this is twice Clara's age in 7 years. Let's denote Clara's current age as \( C \). In 7 years, Clara's age will be \( C + 7 \). According to the problem, we have:
\[ 38 = 2 \times (C + 7) \]
Now, let's solve for Clara's age, \( C \):
1. \( 38 = 2(C + 7) \)
2. \( 38 = 2C + 14 \)
3. \( 38 - 14 = 2C \)
4. \( 24 = 2C \)
5. \( C = 12 \)
So, Clara is currently 12 years old.
Now we can evaluate the statements for Part A regarding Clara’s age:
A) Clara is 12 years old. **(True)**
B) In 14 years, Clara will be 38. \( 12 + 14 = 26 \) **(False)**
C) Clara is 24 years old. **(False)**
D) In 26 years, Clara will be 38. \( 12 + 26 = 38 \) **(True)**
E) In 26 years, Clara will be 50. \( 12 + 26 = 38 \) **(False)**
So, for Part A, the true statements about Clara's age are:
- A (True)
- D (True)
Now let's evaluate Part B concerning Cleo's age:
Cleo is currently 38 years old, and we have established Clara is currently 12 years old.
Now we'll evaluate the statements for Part B:
A) When Clara is 38, Cleo will be 57. \( 38 - 12 = 26 \) years from now; thus, Cleo will be \( 38 + 26 = 64 \). **(False)**
B) When Clara is 38, Cleo will be 64. **(True)**
C) Cleo is 26 years older than Clara. \( 38 - 12 = 26 \). **(True)**
D) Cleo is 14 years older than Clara. **(False)**
E) When Clara is 20, Cleo will be 46. \( 20 - 12 = 8 \), \( 38 + 8 = 46 \). **(True)**
So, for Part B, the true statements about Cleo's age are:
- B (True)
- C (True)
- E (True)
### Summary:
**Part A True Statements**: A, D
**Part B True Statements**: B, C, E