# 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....

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?

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### 1 Answer

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:

0.14*x + *0.14*y* = 0.14*150,000=21,000

0.14*x* +0.29y = 30,000

Subtracting first equation from the second, get

0.15*y* = 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.**