Monica invest a total of $ 17,000 in two accounts. The first account earned a rate of return of 14% (after a year). However, the second account suffered a 9% loss in the same time period. At the end of one year, the total amount of money gained was $ 540.00. How much was invested into each account?

The money invested in the account of gain was x = $ 9,000

The money invested in the account of loss was y = $ 8,000

Step-by-step explanation:

Solution:-

- Monica invested a total T = $ 17,000 in two of her accounts.

- Take the money invested in account A today = x

- Take the money invested in account B today = y

- The total money invested today is:

                      x + y = 17,000   ... Eq1

- After one year, the amount in each categorized by the following statement:

    " The first account earned a rate of return of 14% (after a year) "

- The amount in account A after a year would be = ( 1 + gain/100 )*x

                                                                                 = ( 1 + 14/100)*x

                                                                                 = ( 1 + 0.14 )*x

                                                                                 = 1.14x

The account B:

    " the second account suffered a 9% loss in the same time period "

- The amount in account B after a year would be = ( 1 - loss/100 )*y

                                                                                 = ( 1 - 9/100)*y

                                                                                 = ( 1 - 0.09 )*y

                                                                                 = 0.91*y

- The total amount of money in two accounts after one year would be:

                Total money after a year = 1.14x + 0.91*y

- Given that the gain in one year was G = $540

               G = Total money after one year - Total invested

               540 =  [ 1.14x + 0.91*y ] - 17,000

               17,540 =  1.14x + 0.91*y   Eq 2

- Solve the two equations Eq1 and Eq2 simultaneously:

                x + y = 17,000

               1.14x + 0.91*y = 17,540

             x = $ 9,000 , y = $ 8,000

- The money invested in the account of gain was x = $ 9,000

- The money invested in the account of loss was y = $ 8,000

[2, 2.5)

(2.5, 3]

step-by-step explanation:

i think its these two not sure [2, 2.5)

(2.5, 3]