Question

A person has ​$55,000 invested in stock A and stock B. Stock A currently sells for ​$50 a share and stock B sells for ​$70 a share. If stock B doubles in value and stock A goes up​ 50%, his stock will be worth ​$100,000. How many shares of each stock does he​ own?

Answer 1

This person owns:

• 400 shares of Stock A
• 500 shares of Stock B

Step-by-step explanation:

The person initially has $55,000 invested in stock A and B and they are priced at $50 and $70 respectively, in other words:

• 55000 = 50A + 70B

Where:

• A is the quantity he owns of stock A
• B is the quantity he owns of stock B

Time goes by and the value of A stock goes up %50. This means that it went up to $75, because %50 of 50 is 25, and 25 + 50 is 75.

Also, stock B doubles in value, so it is now selling at $140 and his investment is now worth $100,000, in other words:

• 100000 = 75A + 140B

We have two equations and two unknowns so we can solve the equations to get the values of A and B:

1. 55000 = 50A + 70B
2. 100000 = 75A + 140B

Solve for B on equation 1:

• 
  `B=(55000-50A)/(70)`

Substitute B on equation 2:

• 
  `100000 = 75A + 140(55000-50A)/(70) = 75A + 110000-100A=-25A+110000`

Solve A:

• 
  `A=(100000-110000)/(-25)`
• 
  `A=400`

Now use the value of A in any of the equations to solve for B:

• 
  `B=(55000-50(400))/(70)`
• 
  `B=500`

The amount of shares this person owns of stock A is 400 and 500 of stock B.