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

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