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

Vincen wrote: ↑

Tue Jun 30, 2020 6:44 am

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) \(\frac{y}2 - 6\)
(D) \(\frac{3y}2 - 6\)
(E) \(\frac{5y}2 - 6\)

[spoiler]OA=D[/spoiler]

Source: Official Guide

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