On January 1, 1981, Nick wins $150,000 in the lottery and he invests the entire amount in two stocks, stock X and stock Y. At the end of 1981, he sells both stocks for a total profit of $30,000. If he earned 14% on stock X and 29% of stock Y, how much did he invest in each stock?
The simple interest formula is I = Prt, where P is the principal (amount invested), r is the interest rate expressed as a decimal and t time in years. In this problem time is t = 1 year.
If Nick invested $x in stock X, his interested earned from this stock is `I_x = 0.14x`
If Nick invested $yin stock Y, his interested earned from this stock is `I_y=0.29y`
The total amount invested is x + y = 150,000 and the total interest earned is `I_x+I_y = 0.14x+0.29y = 30,000`
This is a system of equations with two variables. It can be solved by elimination.
Multiply the first equation by 0.14:
0.14x + 0.14y = 0.14*150,000=21,000
0.14x +0.29y = 30,000
Subtracting first equation from the second, get
0.15y = 9,000
`y=9,000/0.15 =60,000 `
Then x = 150,000 - 60,000 = 90,000.
The amount invested in stock X is $90,000 and the amount invested in stock Y is 60,000.