Please please help me with math!!!

Question

You invest a total of $10,400 in two investments earning 5.5% and 10.5% simple intrest. (There is more risk in the 10.5% fund) Your goal is to have a total annual intrest income of $672. Where x represents the amount invested in the 5.5% fund and y represents the amount invested in the 10.5% fund. Solve this system to determine the smallest amount that you can invest at 10.5% in order to meet your objective. 

please help me!!

Answer 1

We will find the solution that will generate exactly $672 in interest income (you can always invest more at 10.5% to try to generate a higher amount).  

 

x + y = 10400  ==>  x = 10400 - y

 

.055*x + .105*y = 672

 

Substitute the value for x in to the 2nd equation 

 

.055*(10400 - y) + .105*y = 672

572 - .055*y + .105*y = 672

.05*y = 100

y = 100 / .05 = 2000

 

So x = 10400 - 2000 = 8400 

 

So the smallest amount you can invest at 10.5% to meet your objective is $2000 

 

Check:  8400 + 2000 = $10400

            .055*8400 + .105*2000 = 462 + 210 = $672 

 

Remember, you can always invest more at 10.5% (and less at 5.5%) to try to earn more interest.  But $2000 is the smallest you can invest at 10.5% to meet your objective.