Price of Basic Computer

BS2009 wrote:
The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/5 of that total. What was the price of the basic computer?

a) $1500
b) $1600
c) $1750
d) $1900
e) $2000

We are given that the total price of a basic computer and a printer was $2,500. If we let a = the price of the basic computer and b = the price of the printer, we can create the following equation:

a + b = 2,500

We are next given that if the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/5 of that total.

If we let the price of the enhanced computer = 500 + a, then we can create the following equation:

(1/5)(500 + a + b) = b

Since a + b = 2,500, we can substitute 2,500 for a + b into the equation (1/5)(500 + a + b) = b.

(1/5)(500 + 2,500) = b

(1/5)(3,000) = b

600 = b

Since b = 600 and a + b = 2,500, we can determine the value of a.

a + 600 = 2,500

a = 1,900

Alternate Solution

The package price of the enhanced computer + printer is $3000. One-fifth of that total is $600, which is the price of the printer by itself. Since the package price of the basic computer + printer is $2,500, we subtract the printer price of $600, getting $1,900 as the price of the basic computer only.

Answer: D