Question

Adam bought three laptops for his office at a total cost of $1,300. The shopkeeper tried to sell Adam some upgrades and accessories that would have doubled the price of the first laptop and tripled the price of the third laptop, increasing the total cost to $2,400. Adam declined to buy the upgrades and accessories as he had already spent a lot on the first laptop, in fact $100 more than the combined price of the second and third laptops. What are the original individual prices of the three laptops?

A.
first laptop: $700
second laptop: $400
third laptop: $200

B.
first laptop: $700
second laptop: $200
third laptop: $400
C.
first laptop: $650
second laptop: $250
third laptop: $400

D.
first laptop: $650
second laptop: $200
third laptop: $450

E.
There is not enough information to solve for the unknowns.

Answer 1

A.

first laptop: $700

second laptop: $400

third laptop: $200

Answer 2

Option: A is the correct answer.

A.

first laptop: $700

second laptop: $400

third laptop: $200

Explanation:

Let the cost of first laptop be: x

Second laptop be: y

and cost of third laptop be: z

Now, it is given that:

Adam bought three laptops for his office at a total cost of $1,300.

This means that:

x+y+z=1300---------(1)

on doubling the price of the first laptop and tripling the price of the third laptop, the total cost increased to $2,400.

This means that:

2x+y+3z=2400-------(2)

He spent $100 more on first laptop than the combined price of the second and third laptops.

This means that:

x-(y+z)=100------------(3)

On using equation (1) we have:

y+z=1300-x

Keeping the value of y+z in equation (3) we get:

x-(1300-x)=100

x-1300+x=100

2x=100+1300

x=1400/2=700

Hence, price of first laptop is: $ 700.

Now on putting the value of x in equation (1) and (2) we get:

y+z=600 ⇒ y=600-z------(4)

and y+3z=1000 (from equation (2) )

⇒ 600-z+3z=1000

⇒ 600+2z=1000

⇒ 2z=1000-600

⇒ 2z=400

⇒ z=200

Hence, cost of third laptop is: $ 200

and cost of second laptop is: $ 400

( since on putting the value of z in equation (4) )