Word problem

Question

You invested $11,000 in stocks and bonds, paying 5% and 8% annual interes. If the total interest earned for the year was $730, how much was invested in stocks and how much was invested in bonds?

Answer 1

Skylar, this uses a system of equations.

 

s + b = 11,000

.05s + .08b = 730

 

First, let's "solve" the first equation for s or b. Let's do s.

 

s = 11,000 - b

 

Next, let's multiply the 2nd by 100 to get rid of those pesky decimals.

 

5s + 8b = 73,000

 

And, let's substitute the "value" for x into our new 2nd equation.

 

5(11,000 - b) + 8b = 73,000

55,000 - 5b + 8b = 73,000

3b = 18,000

b = 6000

 

s = 11,000 - 6000 = 5000

 

You invested $6000 in bonds and $5000 in stocks.

 

 

Answer 2

OK. If we let S = cash spent on shares of stock, and B = cash spent on bonds, then

 

S + B = 11000

 

And the interest is

 

0.05 S + 0.08 B = 730

 

A system of two equations in two unknowns. I multiplied the interest equation by 100,

 

5S + 8B = 73000

 

and the cash by 8,

 

8S + 8B = 88000

 

Then subtracted one equation from the other to eliminate B.

 

3S = 15000

or S = 5000 dollars on stock

so B = 6000 dollars on bonds

 

Cheers!