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?
can anyone help mepls?
To solve this problem, we can set up a system of equations.
Let's assume Shirley has x shares of Boeing stock and y shares of GE stock.
Given information:
Boeing stock price = $30
GE stock price = $70
Total investment = $16,000
Equation 1: The value of the Boeing stock = x * $30
Equation 2: The value of the GE stock = y * $70
According to the problem, after the stock values change, the total investment will be worth $34,500.
So we can create another equation:
Equation 3: The new value of the Boeing stock + the new value of the GE stock = $34,500
Now let's calculate the new values of both stocks:
New value of Boeing stock = (original value of Boeing stock) + 50% * (original value of Boeing stock) = $30 * (1 + 0.50) = $30 * 1.50
New value of GE stock = (original value of GE stock) + 3 * (original value of GE stock) = $70 * (1 + 3) = $70 * 4
Now, we can rewrite Equation 3 using the new stock values:
($30 * 1.50 * x) + ($70 * 4 * y) = $34,500
Using Equation 1, we also know that:
($30 * x) + ($70 * y) = $16,000
Now, we have a system of equations to solve:
($30 * 1.50 * x) + ($70 * 4 * y) = $34,500
($30 * x) + ($70 * y) = $16,000
Solving this system of equations will give us the values of x and y, which represent the number of shares Shirley owns for each stock.