Need help please...

Question

Fatuma invests a total of $11,500 in two accounts paying 10% and 13% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $1,345.00.

 

$ _________ was invested 10% and

 

$ _________ was invested 13% 

Answer 1

Hi Job Allen, to solve this problem, create a system of equations. Let x represent the money invested at 10% and y represent the money invested at 13%.

 

Equation 1:

 

Represents the amount of money invested in the two accounts.

 

x + y = 11500

 

Equation 2:

 

Represents the interest earned in each of the two accounts.

 

.10x  + .13y  = 1345

 

Solve:

 

     x  +       y = 11500

.10x  +  .13y  =  1345

-------------------------

 

Multiply the first equation by -.10

 

 -.10x  -  .10y  = -1150

  .10x  + .13y  =   1345

---------------------------

 

.03y = 195

 

Divide both sides by .03:

 

y = 6500

 

Substitute for y in the first equation:

 

x  +  6500  = 11500

 

Subtract 6500 from both sides:

 

x = 5000

 

Fatuma deposited $5000 in one account and $6500 in the second account.

 

Check:

 

Using equation 2:

 

.10 * 5000 + .13 * 6500 = 1345

 

500 + 845 = 1345

 

1345 = 1345

 

Values check.

 

Questions?