In 2x years from today, a computer will be 75% of (y + 1/2) times its current age. How old is the computer now?

Question

In 2x years from today, a computer will be 75% of (y + 1/2) times its current age. How old is the computer now?

Answer 1

If we let the computer's current age in years = c, then the computer's age in 2x years from today = c + 2x.

The question also says in 2x years the computer's age will be equivalent to 75% of (y + 1/2) * c . As 75% = 3/4 in fractional form, we can we can rewrite this expression as 3/4 * ( y + 1/2 ) * c

As the problem tells us 3/4 * ( y + 1/2 ) * c is equivalent to the computer's age in 2x years, we can create the equation

c + 2x = 3/4 * ( y + 1/2 ) * c

The goal is to isolate the 'c' variable, the computer's current age. So let's move every term with a 'c' to the left hand side of the equation and any term without a 'c' term to the right hand side of the equation. This means, we will subtract 2x from both sides to get

c = 3/4 * ( y + 1/2 ) * c - 2x

And we will subtract 3/4 * ( y + 1/2 ) * c from both sides, resulting in

c - 3/4 * ( y + 1/2 ) * c = -2x

Now, as both terms have "c' on the left hand side of the equation, we can factor out the 'c' giving us

c * ( 1 - [ 3/4 * ( y + 1/2) ] ) = -2x

Distributing the 3/4 gives us

c * ( 1 - [ 3/4 * y + (3/4)*(1/2) ] ) = -2x

c * ( 1 - (3/4 * y) - 3/8 ) = -2x

c * ( 5/8 - (3/4 * y) ) = -2x

Now we can divide both sides by 5/8 - (3/4 * y), giving us

- 2x

c = ________________

5 3y

____ - ____

8 4

Creating a common denominator, 3y/4 = 6y/8,

- 2x

c = ________________

5 6y

____ - ____

8 8

-2x

c = ________________

5 - 6y

_________

8

When dividing by a fraction, the equivalent mathematical operation is to multiply the numerator by the reciprocal of the denominator,

-2x 8

c = _____ * _______

1 5 - 6y

-16x

c = ___________

5 - 6y

Therefore, the current age of the computer in terms of x and y is

-16x

_________

5 - 6y