Word Problem on Stocks

Question

Betty has a total of $18,152 invested in stock A and stock B. Suppose A is currently worth $56 per share and stock B is currently worth $100 per share. If stock A increases by $15 and Stock B increases by $16 her total investment will be worth $21,763. How many shares of each of the stocks does Betty own?

Thank you for your help! I’ve tried looking at different versions of this question but it’s in a way I cannot learn or figure out.

Answer 1

You can solve this problem by creating two equations with two unknowns and solving the equations using elimination.

To start, let's use the variable a to represent the NUMBER of stock A owned and the variable b to represent the NUMBER of stock B owned.

From the part of the problem that states "total of $18,152 invested in stock A and stock B. Suppose A is currently worth $56 per share and stock B is currently worth $100 per share", we can write the following equation:

56a + 100b = 18152

Then since the price of stock A increased by $15 and B increased by $16 for a total of $21763, we can write the following equation (NOTE: 56 + 15 = 71):

71a + 116b = 21763

Now we can solve these two equations using elimination. We can multiply the first equation by 116 and the second equation by -56 as follows. We can then solve for a.

56 a + 100 b = 18152 becomes 6496 a + 1160 0b = 2105632

71 a + 116 b = 21763 becomes -7100 a - 11600 b = -2176300

Now we can solve for a:

6496 a + 11600 b = 2105632

-7100 a - 11600 b = -2176300

-604 a = -70668

-604a/-604 = -70668/-604

a = 117 shares of stock A

For stock B:

56 a + 100 b = 18152

56*117 + 100 b = 18152

6552 + 100 b = 18152

6552 + 100 b - 6552 = 18152 - 6552

100 b = 11600

100b/100 = 11600/100

b = 116

b = 116 shares of stock B