Question

Andrew bought 3 baseball cards for $240.  After a few months, he got an offer from his friend Jack to buy the first card for double its original value, along with either the second or third card.

 Andrew decided to sell the first card (at double its original value) along with the second card (at its original price) and got $320 for it.  Or, selling the first card (at double its original value) card along with the third card (at its original price) would have only got him $280.  What were the original prices for each of the 3 baseball cards?

(80, 120, 40) (80, 130, 30)
(130, 90, 20)
(120, 80, 40)

Answer 1

First we define variables:
x = first card original value
y = second card original value
z = third card original value
We write the system of equations:
Andrew bought 3 baseball cards for $ 240:
x + y + z = 240
the first card (at its original value) along with the second card (at its original price) and got $ 320:
2x + y = 320
the first card (at its original value) card along with the third card (at its original price) would have only got him $ 280:
2x + z = 280
Solving the system we have:
x = 120
y = 80
z = 40
Answer:
The original prices for each of the 3 baseball cards is:
(120, 80, 40)