Question

Mrs Kokomo invested k30000;part at 5% and part at 8%.The total interest on the investment was k2100. How much did she invest at each rate?​

Answer 1

To determine the amount Mrs. Kokomo invested at each interest rate, a system of equations is set up and solved with the substitution method, revealing that she invested K10000 at 5% and K20000 at 8%.

Step-by-step explanation:

Mrs. Kokomo invested a total of K30000 at two different interest rates: one part at 5% and one part at 8%. The total interest earned from these investments was K2100. To determine how much was invested at each rate, we can set up a system of equations based on the given information. Let's represent the amount invested at 5% as x and the amount invested at 8% as y. Therefore, we have two equations:

1. 
   
3. x + y = 30000 (because the total investment is K30000)
4. 
   
6. 0.05x + 0.08y = 2100 (the total interest from the investments)

To solve this system, we can use substitution or elimination. Subtracting equation (1) from equation (2) after multiplying by appropriate factors could allow elimination or solving equation (1) for one variable and substituting into equation (2) for substitution. After finding values for x and y, we'll know how much was invested at each rate.

Let's demonstrate the substitution method for solving:

1. 
   
3. x = 30000 - y (rearranging equation (1))
4. 
   
6. Substitute x in equation (2): 0.05(30000 - y) + 0.08y = 2100
7. 
   
9. Simplify and solve for y: 1500 - 0.05y + 0.08y = 2100
10. 
    
12. Combine like terms: 0.03y = 600
13. 
    
15. Solve for y: y = 20000
16. 
    
18. Substitute y back into equation to find x: x = 30000 - 20000 = 10000

Therefore, Mrs. Kokomo invested K10000 at 5% and K20000 at 8%.