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?

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