a woman has $28,000. part is invested for one year in a certificate of deposit paying 7% interest, and the remaining amount in cash management fund paying 9%. after 1 year, the total interest on the two investments is $2,200. how much is invested at each rate

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ApusApus ApusApus · Answer 1 · 2018-10-18T06:37:08+02:00

Answer:

Amount invested at 7% = 16000

Amount invested at 9% = 12000

Step-by-step explanation:

Let x be the amount invested at 7% and y be the amount invested at 9%.

Since the total amount invested is $28000, therefore, we can set up the first equation as:

[tex]x+y=28000[/tex]

Secondly, we are give that sum of two investments is $2200. Therefore, we can write the second equation as:

[tex]0.07x+0.09y=2200[/tex]

Now we need to solve these two equations to get the values of x and y.

First of all, we multiply the second equation with 100 in order to get rid of decimal values.

[tex](0.07x+0.09y)*100=2200*100\\7x+9y=220000[/tex]

Let us use substitution method here. First of all we will solve for y from first equation and plug that into second equation.

[tex]y=28000-x[/tex]

[tex]7x+9(28000-x)=220000\\7x+252000-9x=220000\\-2x=-32000\\x=16000[/tex]

Therefore, amount invested at 7% is $16000 and amount invested at 9% is 28000-16000=$12000.