Shirley has $16,000 invested in Boeing and GE stock. The Boeing stock currently sells for $30 a share and the GE stock for $70 a share. If GE stock triples in value and Boeing stock goes up 50%, her stock will be worth $34,500. how many shares of each stock does she own?

To solve this problem, let's assume that Shirley owns x shares of Boeing stock and y shares of GE stock.

According to the given information, we know that Shirley has $16,000 invested in total. So, we can set up the following equation:

30x + 70y = 16,000

Next, let's evaluate the value of her stock after the increase in value.

The stock price of Boeing increases by 50%. Therefore, after the increase, the price per share of Boeing stock will be 1.5 * $30 = $45.

The stock price of GE triples, so it will be 3 * $70 = $210 per share.

According to the new total value of her stock ($34,500), we can set up a second equation:

45x + 210y = 34,500

Now we have two equations:

30x + 70y = 16,000 ----(1)
45x + 210y = 34,500 ----(2)

We can solve these equations simultaneously to find the values of x and y.

First, let's multiply equation (1) by 3:

90x + 210y = 48,000 ----(3)

Subtract equation (3) from equation (2):

45x + 210y - (90x + 210y) = 34,500 - 48,000

Simplifying, we get:

-45x = -13,500

Dividing by -45 on both sides:

x = 13,500 / 45

x = 300

Now, substitute the value of x back into equation (1):

30(300) + 70y = 16,000

9,000 + 70y = 16,000

Subtract 9,000 from both sides:

70y = 7,000

Divide by 70 on both sides:

y = 7,000 / 70

y = 100

Therefore, Shirley owns 300 shares of Boeing stock and 100 shares of GE stock.

Let's assume that Shirley owns x shares of Boeing stock and y shares of GE stock.

Given that the Boeing stock sells for $30 a share, the total value of her Boeing investment is 30 * x dollars.

Similarly, the total value of her GE investment is 70 * y dollars.

According to the given information, the total value of her stocks after GE stock triples in value and Boeing stock goes up 50% is $34,500.

Therefore, we can write the equation:

30 * x + 70 * y = 34,500

Now, let's look at the relationship between the number of shares and the increase in value:

The GE stock triples in value, so the new value of the GE investment is 3 * 70 * y.

The Boeing stock goes up 50%, so the new value of the Boeing investment is 1.5 * 30 * x.

The sum of these new values must equal $34,500:

3 * 70 * y + 1.5 * 30 * x = 34,500

Simplifying the equation, we have:

210y + 45x = 34,500

Now we have a system of two equations:

30x + 70y = 34,500 (Equation 1)
45x + 210y = 34,500 (Equation 2)

To solve this system, we can multiply Equation 1 by 3 and Equation 2 by 2 to eliminate the coefficients of x:

90x + 210y = 103,500 (Equation 3)
90x + 420y = 69,000 (Equation 4)

By subtracting Equation 3 from Equation 4, we can eliminate x and solve for y:

(90x + 420y) - (90x + 210y) = 69,000 - 103,500
210y - 210y = -34,500
0 = -34,500

Since this equation is not true, there is no solution to the system. This suggests that the given information is inconsistent or there is an error in the problem statement. Please check the given information and calculations.