Question

Ed is 7 years older than Ted. Ed’s age is also 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.
which one is it A, B, C or D

Answer 1

Given:

Given that, Ed is 7 years older than Ted and Ed’s age is $\frac{3}{2}$ times Ted’s age.

To find:

We need to find the age of Ted and Ed.

Solution:

Let the age of Ed is $x$.

And the age of Ted is $y$.

According to the question, Ed is 7 years older than Ted.

Writing the above statement in the form of a equation,

$\Rightarrow x=7+y$....(i)

Also, Ed’s age is $\frac{3}{2}$ times Ted’s age.

Writing the above statement in the form of a equation,

$\Rightarrow x=\frac{3}{2 }y$....(ii)

Now equate equation (i) and equation (ii).

$\Rightarrow 7+y=\frac{3}{2} y$

$\Rightarrow 7=\frac{3}{2} y-y$

$\Rightarrow 7=\frac{3y-2y}{2}$

$\Rightarrow 7=\frac{y}{2}$

$\Rightarrow 7\times 2=y$

$\Rightarrow 14=y$

$\Rightarrow y=14$....(iii)

Now substitute equation (iii) in equation (i).

$\Rightarrow x=7+y$

$\Rightarrow x=7+14$

$\Rightarrow x=21$

Therefore, Ted is 14 years old and Ed is 21 years old (Option B).