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27 November, 14:12

Rachel Dawkins has $26,000 invested in stock A and stock B. Stock A currently sells for $50 a share and stock B sells for $60 a share. If stock B doubles in value and stock A goes up 50%, her stock will be worth $42,000. How many shares of each stock does she own?

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Answers (2)
  1. 27 November, 14:19
    0
    Stock A = 400 and Stock B = 100

    Explanation:

    Rachel invested $26,000 in stock A and stock B at $50 and $60 respectively. The first equation will be:

    ⇒ 26,000 = A50 + B60 (equation 1)

    After some time,

    The stock A increases by 50% which means the value of stock A currently is (50 x 150%) = $75 The stock B doubles in value which means the value of stock B currently is (60 x 2) = $120

    The total worth of the both stock is now $42,000. The second equation will be:

    ⇒ 42,000 = A75 + B120 (equation 2)

    We have 2 equations now,

    ⇒ 26,000 = A50 + B60 (equation 1)

    ⇒ 42,000 = A75 + B120 (equation 2)

    To solve this, multiply equation 1 by - 2,

    ⇒ (-2 x 26,000) = (-2 x A50) + (-2 x B60)

    ⇒ - 52,000 = - A100 - B120 (equation 3)

    Solve equation 2 and 3 to compute the value of A:

    ⇒ 42,000 = A75 + B120

    ⇒ - 52,000 = - A100 - B120

    ⇒ - 10,000 = - A25

    ⇒ A = - 10,000/-25

    ⇒ A = 400

    Substitute the value of A in any of the above equation to compute B, let's say in equation 1:

    ⇒ 26,000 = A50 + B60

    ⇒ 26,000 = (400) 50 + B60

    ⇒ 26,000 = 20,000 + B60

    ⇒ B60 = 26,000 - 20,000

    ⇒ B60 = 6,000

    ⇒ B = 6,000/60

    ⇒ B = 100
  2. 27 November, 14:32
    0
    The Stock A = 400 and Stock B = 100

    Explanation:

    From the question given, we solve the problem as stated

    Rachel invested $26,000 in stock A and stock B at prices of $50 and $60 respectively.

    The first equation is given as:

    26,000 = A50 + B60

    Then,

    After a while, the stock A increases by 50% this means that,

    the value of stock A currently is (50 x 150%) = $75

    The stock B increases in value this means,

    The current value of stock B is (60 x 2) = $120

    The total stock both are worth is $42,000.

    Thus,

    The second equation becomes:

    42,000 = A75 + B120

    We now have 2 equations.

    The Equation 1 is denoted as:

    26,000 = A50 + B60 (equation 1)

    The equation 2 is denoted as:

    42,000 = A75 + B120 (equation 2)

    To Further solve this, we multiply equation 1 by - 2,

    Which is,

    (-2 x 26,000) = (-2 x A50) + (-2 x B60)

    52,000 = - A100 - B120 (equation 3)

    Solve equation 2 and 3 to get the value of A:

    42,000 = A75 + B120

    -52,000 = - A100 - B120

    -10,000 = - A25

    A = - 10,000/-25

    A = 400

    Substitute the value of A in any of the equation to get B,

    So,

    26,000 = A50 + B60

    26,000 = (400) 50 + B60

    26,000 = 20,000 + B60

    B60 = 26,000 - 20,000

    B60 = 6,000

    B = 6,000/60

    Therefore, B = 100
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Home » Business » Rachel Dawkins has $26,000 invested in stock A and stock B. Stock A currently sells for $50 a share and stock B sells for $60 a share. If stock B doubles in value and stock A goes up 50%, her stock will be worth $42,000.
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