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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?

Respuesta :

Answer:

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

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Answer:

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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