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Question 509032: Sandy has an investment account with shares in two companies, SMT and KLR. At the end of June, when each share of SMT was worth $9 and each share of KLR was worth $8, Sandys account was worth $1600. Three months later, SMT was worth $7 a share, KLR was worth $16 a share, and Sandys account was worth $2320. Find the number of shares that Sandy owns for each of the two companies and determine the value of her account when SMT is priced at $11 a share and KLR is priced at $10 a share
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = number of shares of SMT
let y = number of shares of KLR
9x + 8y = 1600 (first equation)
7x + 16y = 2320 (second equation)
solve these 2 equations simultaneously to get the value of x and y.
multiply first equation by 2 to get:
2 * (9x + 8y) = 2 * 1600 which becomes:
18x + 16y = 3200 (third equation)
subtract second equation from third equation to get:
18x + 16y = 3200 minus:
7x + 16y = 2320 becomes:
11x = 880
divide both sides of this equation by 11 to get:
x = 80
substitute 80 for x in first equation to get:
720 + 8y = 1600
subtract 720 from both sides of this equation to get:
8y = 1600 - 720 = 880
divide both sides of this equation to get:
y = 110
you have:
x = 80
y = 110
this means that:
number of shares of SMT = 80
number of shares of KLR = 110
plug these values into your original equations to confirm they are good.
9x + 8y = 1600 (first equation)
7x + 16y = 2320 (second equation)
become:
9*80 + 8*110 = 1600 (first equation)
7*80 + 16*110 = 2320 (second equation)
simplify to get:
1600 = 1600 (first equation)
2320 = 2320 (second equation)
values are confirmed to be good.
when SMT is equal to $11 a share and KLR is equal to $10 a share, the equation becomes:
11*80 + 10*110 = 880 + 1100 = $1980
that's your answer.
number of shares of SMT is 80
number of shares of KLR is 110
value of portfolio when SMT is $11 a share and KLR is $10 a share is $1980.
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