Question

5
select the correct answer
ed is 7 years older than ted. ed’s age is also \\(\frac{3}{2}\\) times ted’s age. how old are ed and ted?
a. ted is 15 years old, and ed is 22 years old.
b. ted is 14 years old, and ed is 21 years old.
c. ted is 13 years old, and ed is 20 years old.
d. ted is 12 years old, and ed is 19 years old.

Explanation:

Step1: Let Ted's age be \( x \). Then Ed's age is \( x + 7 \) (since Ed is 7 years older) and also \( \frac{3}{2}x \) (from the problem statement).

So we set up the equation: \( x + 7=\frac{3}{2}x \)

Step2: Solve the equation. Subtract \( x \) from both sides: \( 7=\frac{3}{2}x - x=\frac{1}{2}x \)

Multiply both sides by 2: \( x = 14 \)
Then Ed's age is \( 14 + 7 = 21 \) or \( \frac{3}{2}\times14 = 21 \)
We can also check each option:

• Option A: Ted = 15, Ed = 22. \( 22-15 = 7 \), but \( \frac{22}{15}

eq\frac{3}{2} \).

• Option B: Ted = 14, Ed = 21. \( 21 - 14 = 7 \), and \( \frac{21}{14}=\frac{3}{2} \).
• Option C: Ted = 13, Ed = 20. \( 20 - 13 = 7 \), but \( \frac{20}{13}

eq\frac{3}{2} \).

• Option D: Ted = 12, Ed = 19. \( 19 - 12 = 7 \), but \( \frac{19}{12}

eq\frac{3}{2} \).

Answer:

B. Ted is 14 years old, and Ed is 21 years old.