In a certain month, Nortel (NT) stock started and ended the month valued at $4.70 a share, and Altria Group (MO) increased from $48 to $52 a share. If you invested a total of $5,458 in these stocks at the beginning of this month and sold them for $5,858 at the end of this month, how many shares of each stock did you buy ?
A)130 shares of NT and 120 shares of MO
B) 140 shares of NT and 100 shares of MO
C) 101 shares of NT and 254 shares of MO
D) 100 shares of NT and 140 shares of MO
E) 130 shares of NT and 470 shares of MO

Question

In a certain month, Nortel (NT) stock started and ended the month valued at $4.70 a share, and Altria Group (MO) increased from $48 to $52 a share. If you invested a total of $5,458 in these stocks at the beginning of this month and sold them for $5,858 at the end of this month, how many shares of each stock did you buy  ?
A)130 shares of NT and 120 shares of MO
B) 140 shares of NT and 100 shares of MO
C) 101 shares of NT and 254 shares of MO
D) 100 shares of NT and 140 shares of MO
E) 130 shares of NT and 470 shares of MO

Quizplus · Accepted Answer

Let x be the number of shares of Nortel (NT) stock and y be the number of shares of Altria Group (MO) stock.
Then we have two equations: 
4.7x + 48y = 5458 (the total amount invested)
4.7x + 52y = 5858 (the total amount received)
Subtracting the first equation from the second, we get:
4y = 400
y = 100
Plugging y = 100 into either equation, we get:
4.7x + 4800 = 5458 
4.7x = 658 
x ≈ 139.15
Since we can only buy whole shares, we buy 140 shares of Nortel and 100 shares of Altria, which adds up to $5458. At the end of the month, the value of these shares are:
140 shares of Nortel = $658
100 shares of Altria = $520
Total = $1178
This means we gained $400 from the investment, bringing the total to $5858.

In a Certain Month, Nortel (NT) Stock Started and Ended