The sum of the ages of Doris and Fred is y years. If Doris

BTGmoderatorDC wrote:The sum of the ages of Doris and Fred is y years. If Doris is 12 years older than Fred , how many years old will Fred be y years from now, in terms of y ?

(A) y - 6
(B) 2y - 6
(C) y/2 - 6
(D) 3y/2 - 6
(E) 5y/2 - 6

OA D

Source: Official Guide

Say Dory's age be D and Fred's age be F years. Thus, we have D + F = y. Also given that D = F + 12. Thus, 2F + 12 = y => F = (y – 12)/2 = y/2 – 6

Fred y years from now = F + y = y/2 – 6 + y = 3y/2 – 6

The correct answer: D

Hope this helps!

-Jay
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BTGmoderatorDC wrote:The sum of the ages of Doris and Fred is y years. If Doris is 12 years older than Fred , how many years old will Fred be y years from now, in terms of y ?

(A) y - 6
(B) 2y - 6
(C) y/2 - 6
(D) 3y/2 - 6
(E) 5y/2 - 6

Let F = Fred's PRESENT age

Doris is 12 years older than Fred.
In other words, Doris' age = F + 12.
So, the sum of their ages = F + (F + 12)
Simplify to get: sum of their ages = 2F + 12

The sum of the ages = y
2F + 12 = y

Now solve for Fred's age (F).
Start with: 2F + 12 = y
Subtract 12 form both sides: 2F = y - 12
Divide both sides by 2 to get: F = (y - 12)/2
Rewrite as: F = y/2 - 12/2
Simplify: F = y/2 - 6
So, Fred's PRESENT age is y/2 - 6

How many years old will Fred be y years from now, in terms of y?
Add y to Frank's PRESENT age to get: y/2 - 6 + y

Check the answer choices . . . y/2 - 6 + y isn't there!
Looks like we need to SIMPLIFY

y/2 - 6 + y = y/2 - 6 + 2y/2 (get common denominator of 2)
= 3y/2 - 6
= D

Cheers,
Brent

BTGmoderatorDC wrote:The sum of the ages of Doris and Fred is y years. If Doris is 12 years older than Fred , how many years old will Fred be y years from now, in terms of y ?

(A) y - 6
(B) 2y - 6
(C) y/2 - 6
(D) 3y/2 - 6
(E) 5y/2 - 6



OA D

Source: Official Guide

We can let Doris’s age today = d and Fred’s age today = f and create the following equations:

d + f = y

and

d = 12 + f

Substituting, we have:

12 + f + f = y

2f = y - 12

f = (y - 12)/2

So y years from now Fred will be:

(y - 12)/2 + y = (y - 12)/2 + 2y/2 = (3y - 12)/2 = 3y/2 - 6

Answer: D