An investor invested a total of $2,800 in two mutual funds. One fund earned 5% profit while the other earned 3% profit. If the investor's total profit was $104, how much was invested in each mutual fund? The amount invested in the mutual fund that earned 5% was $(blank). The amount invested in the mutual fund that earned 3% was $(blank). (show your work)

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calculista calculista · Answer 1 · 2019-12-06T21:00:40+01:00

Answer:

The amount invested in the mutual fund that earned 5% was $1,000

The amount invested in the mutual fund that earned 3% was $1,800

Step-by-step explanation:

Let

x ----> the amount invested in the mutual fund that earned 5%

y ----> the amount invested in the mutual fund that earned 3%

we know that

[tex]x+y=2,800[/tex] ----> [tex]y=2,800-x[/tex] ----> equation A

[tex]5\%=5/100=0.05[/tex]

[tex]3\%=3/100=0.03[/tex]

[tex]0.05x+0.03y=104[/tex] ----> equation B

Solve the system by substitution

substitute equation A in equation B

[tex]0.05x+0.03(2,800-x)=104[/tex]

Solve for x

[tex]0.05x+84-0.03x=104[/tex]

[tex]0.05x-0.03x=104-84[/tex]

[tex]0.02x=20[/tex]

[tex]x=\$1,000[/tex]

Find the value of y

[tex]y=2,800-x[/tex]

[tex]y=2,800-1,000=\$1,800[/tex]

therefore

The amount invested in the mutual fund that earned 5% was $1,000 and the amount invested in the mutual fund that earned 3% was $1,800