Select the correct answer.
Ed is 7 years older than Ted. Ed’s age is also 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.
B. Ted is 14 years old, and Ed is 21 years old.
Let's solve this step-by-step!
Let's assume Ted's age as "x".
According to the given information, Ed is 7 years older than Ted, so Ed's age is "x + 7".
Also, Ed's age is 3/2 times Ted's age, so we have the equation:
(x + 7) = (3/2)x
We can simplify this equation by multiplying both sides by 2 to eliminate the fraction:
2(x + 7) = 3x
2x + 14 = 3x
Now, let's subtract 2x from both sides to get all the "x" terms on one side:
14 = x
So, Ted is 14 years old.
Substituting this value of x in the equation we assumed for Ed's age:
Ed = x + 7 = 14 + 7 = 21
Therefore, Ted is 14 years old, and Ed is 21 years old.
So, the correct answer is B. Ted is 14 years old, and Ed is 21 years old.