example 2 Investment

Chapter 7.2

The Trust Department of Century Bank divided a $150,000 investment among threemutual funds with different levels of risk and return. The Potus Fund returns 10% peryear, the Stong Fund returns 8% per year, and the Franklin Fund returns 7%. If theannual return from the combined investments is $12,900 and if the investment in thePotus Fund has $20,000 less than the sum of the investments in the other two funds,how much is invested in each fund?

2009 PBLPathways

2009 PBLPathways

The Trust Department of Century Bank divided a $150,000 investment among threemutual funds with different levels of risk and return. The Potus Fund returns 10% peryear, the Stong Fund returns 8% per year, and the Franklin Fund returns 7%. If theannual return from the combined investments is $12,900 and if the investment in thePotus Fund has $20,000 less than the sum of the investments in the other two funds,how much is invested in each fund?

2009 PBLPathways

The Trust Department of Century Bank divided a $150,000 investment among threemutual funds with different levels of risk and return. The Potus Fund returns 10% peryear, the Stong Fund returns 8% per year, and the Franklin Fund returns 7%. If theannual return from the combined investments is $12,900 and if the investment in thePotus Fund has $20,000 less than the sum of the investments in the other two funds,how much is invested in each fund?

x: Amount invested in the Potus Fundy: Amount invested in the Stong Fundz: Amount invested in the Franklin Fund

2009 PBLPathways

The Trust Department of Century Bank divided a $150,000 investment among threemutual funds with different levels of risk and return. The Potus Fund returns 10% peryear, the Stong Fund returns 8% per year, and the Franklin Fund returns 7%. If theannual return from the combined investments is $12,900 and if the investment in thePotus Fund has $20,000 less than the sum of the investments in the other two funds,how much is invested in each fund?

x: Amount invested in the Potus Fundy: Amount invested in the Stong Fundz: Amount invested in the Franklin Fund

2009 PBLPathways

The Trust Department of Century Bank divided a $150,000 investment among threemutual funds with different levels of risk and return. The Potus Fund returns 10% peryear, the Stong Fund returns 8% per year, and the Franklin Fund returns 7%. If theannual return from the combined investments is $12,900 and if the investment in thePotus Fund has $20,000 less than the sum of the investments in the other two funds,how much is invested in each fund?

x: Amount invested in the Potus Fundy: Amount invested in the Stong Fundz: Amount invested in the Franklin Fund

150,000

0.10 0.08 0.07 12,900

20,000

x y z

x y z

x y z

Sum of the investments

Total annual return

2009 PBLPathways

The Trust Department of Century Bank divided a $150,000 investment among threemutual funds with different levels of risk and return. The Potus Fund returns 10% peryear, the Stong Fund returns 8% per year, and the Franklin Fund returns 7%. If theannual return from the combined investments is $12,900 and if the investment in thePotus Fund has $20,000 less than the sum of the investments in the other two funds,how much is invested in each fund?

x: Amount invested in the Potus Fundy: Amount invested in the Stong Fundz: Amount invested in the Franklin Fund

150,000

0.10 0.08 0.07 12,900

20,000

x y z

x y z

x y z

Sum of the investments

Total annual return

2009 PBLPathways

The Trust Department of Century Bank divided a $150,000 investment among threemutual funds with different levels of risk and return. The Potus Fund returns 10% peryear, the Stong Fund returns 8% per year, and the Franklin Fund returns 7%. If theannual return from the combined investments is $12,900 and if the investment in thePotus Fund has $20,000 less than the sum of the investments in the other two funds,how much is invested in each fund?

x: Amount invested in the Potus Fundy: Amount invested in the Stong Fundz: Amount invested in the Franklin Fund

150,000

0.10 0.08 0.07 12,900

20,000

x y z

x y z

x y z

Sum of the investments

Total annual return

2009 PBLPathways

The Trust Department of Century Bank divided a $150,000 investment among threemutual funds with different levels of risk and return. The Potus Fund returns 10% peryear, the Stong Fund returns 8% per year, and the Franklin Fund returns 7%. If theannual return from the combined investments is $12,900 and if the investment in thePotus Fund has $20,000 less than the sum of the investments in the other two funds,how much is invested in each fund?

x: Amount invested in the Potus Fundy: Amount invested in the Stong Fundz: Amount invested in the Franklin Fund

150,000

0.10 0.08 0.07 12,900

20,000

x y z

x y z

x y z

Total annual return

2009 PBLPathways

The Trust Department of Century Bank divided a $150,000 investment among threemutual funds with different levels of risk and return. The Potus Fund returns 10% peryear, the Stong Fund returns 8% per year, and the Franklin Fund returns 7%. If theannual return from the combined investments is $12,900 and if the investment in thePotus Fund has $20,000 less than the sum of the investments in the other two funds,how much is invested in each fund?

x: Amount invested in the Potus Fundy: Amount invested in the Stong Fundz: Amount invested in the Franklin Fund

150,000

0.10 0.08 0.07 12,900

20,000

x y z

x y z

x y z

2009 PBLPathways

The Trust Department of Century Bank divided a $150,000 investment among threemutual funds with different levels of risk and return. The Potus Fund returns 10% peryear, the Stong Fund returns 8% per year, and the Franklin Fund returns 7%. If theannual return from the combined investments is $12,900 and if the investment in thePotus Fund has $20,000 less than the sum of the investments in the other two funds,how much is invested in each fund?

x: Amount invested in the Potus Fundy: Amount invested in the Stong Fundz: Amount invested in the Franklin Fund

150,000

0.10 0.08 0.07 12,900

20,000

x y z

x y z

x y z

2009 PBLPathways

The Trust Department of Century Bank divided a $150,000 investment among threemutual funds with different levels of risk and return. The Potus Fund returns 10% peryear, the Stong Fund returns 8% per year, and the Franklin Fund returns 7%. If theannual return from the combined investments is $12,900 and if the investment in thePotus Fund has $20,000 less than the sum of the investments in the other two funds,how much is invested in each fund?

x: Amount invested in the Potus Fundy: Amount invested in the Stong Fundz: Amount invested in the Franklin Fund

150,000

0.10 0.08 0.07 12,900

20,000

x y z

x y z

x y z

2009 PBLPathways

The Trust Department of Century Bank divided a $150,000 investment among threemutual funds with different levels of risk and return. The Potus Fund returns 10% peryear, the Stong Fund returns 8% per year, and the Franklin Fund returns 7%. If theannual return from the combined investments is $12,900 and if the investment in thePotus Fund has $20,000 less than the sum of the investments in the other two funds,how much is invested in each fund?

x: Amount invested in the Potus Fundy: Amount invested in the Stong Fundz: Amount invested in the Franklin Fund

150,000

0.10 0.08 0.07 12,900

20,000

x y z

x y z

x y z

2009 PBLPathways

The Trust Department of Century Bank divided a $150,000 investment among threemutual funds with different levels of risk and return. The Potus Fund returns 10% peryear, the Stong Fund returns 8% per year, and the Franklin Fund returns 7%. If theannual return from the combined investments is $12,900 and if the investment in thePotus Fund has $20,000 less than the sum of the investments in the other two funds,how much is invested in each fund?

150,000

0.10 0.08 0.07 12,900

20,000

x y z

x y z

x y z

150,000

0.10 0.08 0.07 12,900

20,000

x y z

x y z

x y z

2009 PBLPathways

The Trust Department of Century Bank divided a $150,000 investment among threemutual funds with different levels of risk and return. The Potus Fund returns 10% peryear, the Stong Fund returns 8% per year, and the Franklin Fund returns 7%. If theannual return from the combined investments is $12,900 and if the investment in thePotus Fund has $20,000 less than the sum of the investments in the other two funds,how much is invested in each fund?

1 1 1 150,000

0.10 0.08 0.07 12,900

1 1 1 20,000

1 0 0 ?

0 1 0 ?

0 0 1 ?

2009 PBLPathways

1 1 1 150,000

0.10 0.08 0.07 12,900

1 1 1 20,000

1 0 0 ?

0 1 0 ?

0 0 1 ?

The Trust Department of Century Bank divided a $150,000 investment among threemutual funds with different levels of risk and return. The Potus Fund returns 10% peryear, the Stong Fund returns 8% per year, and the Franklin Fund returns 7%. If theannual return from the combined investments is $12,900 and if the investment in thePotus Fund has $20,000 less than the sum of the investments in the other two funds,how much is invested in each fund?

2009 PBLPathways

1 1 1 150,000

0.10 0.08 0.07 12,900

1 1 1 20,000

1 0 0 ?

0 1 0 ?

0 0 1 ?

The Trust Department of Century Bank divided a $150,000 investment among threemutual funds with different levels of risk and return. The Potus Fund returns 10% peryear, the Stong Fund returns 8% per year, and the Franklin Fund returns 7%. If theannual return from the combined investments is $12,900 and if the investment in thePotus Fund has $20,000 less than the sum of the investments in the other two funds,how much is invested in each fund?

2009 PBLPathways

1 1 1 150,000

0.10 0.08 0.07 12,900

1 1 1 20,000

1 0 0 ?

0 1 0 ?

0 0 1 ?

The Trust Department of Century Bank divided a $150,000 investment among threemutual funds with different levels of risk and return. The Potus Fund returns 10% peryear, the Stong Fund returns 8% per year, and the Franklin Fund returns 7%. If theannual return from the combined investments is $12,900 and if the investment in thePotus Fund has $20,000 less than the sum of the investments in the other two funds,how much is invested in each fund?

2009 PBLPathways

1 1 1 150,000

0.10 0.08 0.07 12,900

1 1 1 20,000

1 0 0 ?

0 1 0 ?

0 0 1 ?

The Trust Department of Century Bank divided a $150,000 investment among threemutual funds with different levels of risk and return. The Potus Fund returns 10% peryear, the Stong Fund returns 8% per year, and the Franklin Fund returns 7%. If theannual return from the combined investments is $12,900 and if the investment in thePotus Fund has $20,000 less than the sum of the investments in the other two funds,how much is invested in each fund?

2009 PBLPathways

1 1 1 150,000

0.10 0.08 0.07 12,900

1 1 1 20,000

-0.10 R1 + R2 R2- R1 + R3 R3

2 2 4 6

2 3 1 1

0 1 3 5

1 1 1 150,000

0 0.02 0.03 2,100

0 2 2 170,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

-50 R2 R2

- R2 + R1 R12R2 + R3 R3

2 2 4 6

2 3 1 1

0 1 3 5

1 0 0.5 45,000

0 1 1.5 105,000

0 0 1 40,000

2009 PBLPathways

1 1 1 150,000

0.10 0.08 0.07 12,900

1 1 1 20,000

-0.10 R1 + R2 R2- R1 + R3 R3

0.1 0.1 0.1 15,000

0.10 0.08 0.07 12,900

0 0.02 0.03 2100

1 1 1 150,000

0 0.02 0.03 2,100

0 2 2 170,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

-50 R2 R2

2009 PBLPathways

1 1 1 150,000

0.10 0.08 0.07 12,900

1 1 1 20,000

-0.10 R1 + R2 R2- R1 + R3 R3

0.1 0.1 0.1 15,000

0.10 0.08 0.07 12,900

0 0.02 0.03 2100

1 1 1 150,000

0 0.02 0.03 2,100

0 2 2 170,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

-50 R2 R2

2009 PBLPathways

1 1 1 150,000

0.10 0.08 0.07 12,900

1 1 1 20,000

-0.10 R1 + R2 R2- R1 + R3 R3

0.1 0.1 0.1 15,000

0.10 0.08 0.07 12,900

0 0.02 0.03 2100

1 1 1 150,000

0 0.02 0.03 2,100

0 2 2 170,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

-50 R2 R2

2009 PBLPathways

1 1 1 150,000

0.10 0.08 0.07 12,900

1 1 1 20,000

-0.10 R1 + R2 R2-1 R1 + R3 R3

1 1 1 150,000

1 1 1 20,000

0 2 2 170,000

1 1 1 150,000

0 0.02 0.03 2,100

0 2 2 170,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

-50 R2 R2

2009 PBLPathways

1 1 1 150,000

0.10 0.08 0.07 12,900

1 1 1 20,000

-0.10 R1 + R2 R2-1 R1 + R3 R3

1 1 1 150,000

1 1 1 20,000

0 2 2 170,000

1 1 1 150,000

0 0.02 0.03 2,100

0 2 2 170,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

-50 R2 R2

2009 PBLPathways

1 1 1 150,000

0.10 0.08 0.07 12,900

1 1 1 20,000

-0.10 R1 + R2 R2-1 R1 + R3 R3

1 1 1 150,000

1 1 1 20,000

0 2 2 170,000

1 1 1 150,000

0 0.02 0.03 2,100

0 2 2 170,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

-50 R2 R2

2009 PBLPathways

1 1 1 150,000

0.10 0.08 0.07 12,900

1 1 1 20,000

-0.10 R1 + R2 R2-1 R1 + R3 R3

1 1 1 150,000

1 1 1 20,000

0 2 2 170,000

1 1 1 150,000

0 0.02 0.03 2,100

0 2 2 170,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

-50 R2 R2

2009 PBLPathways

1 1 1 150,000

0.10 0.08 0.07 12,900

1 1 1 20,000

-0.10 R1 + R2 R2-1 R1 + R3 R3

1 1 1 150,000

1 1 1 20,000

0 2 2 170,000

1 1 1 150,000

0 0.02 0.03 2,100

0 2 2 170,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

-50 R2 R2

2009 PBLPathways

0.5 R3 + R1 R1-1.5 R3 + R2 R2

2 2 4 6

2 3 1 1

0 1 3 5

1 0 0 65,000

0 1 0 45,000

0 0 1 40,000

65,000

45,000

40,000

x

y

z

Invest $65,000 in the Potus Fund

Invest $45,000 in the Stong Fund

Invest $40,000 in the Franklin Fund

- R2 + R1 R12R2 + R3 R3

2 2 4 6

2 3 1 1

0 1 3 5

1 0 0.5 45,000

0 1 1.5 105,000

0 0 1 40,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

2009 PBLPathways

0.5 R3 + R1 R1-1.5 R3 + R2 R2

2 2 4 6

2 3 1 1

0 1 3 5

1 0 0 65,000

0 1 0 45,000

0 0 1 40,000

65,000

45,000

40,000

x

y

z

Invest $65,000 in the Potus Fund

Invest $45,000 in the Stong Fund

Invest $40,000 in the Franklin Fund

-1 R2 + R1 R12R2 + R3 R3

0 1 1.5 105,000

1 1 1 150,000

1 0 0.5 45,000

1 0 0.5 45,000

0 1 1.5 105,000

0 0 1 40,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

2009 PBLPathways

0.5 R3 + R1 R1-1.5 R3 + R2 R2

2 2 4 6

2 3 1 1

0 1 3 5

1 0 0 65,000

0 1 0 45,000

0 0 1 40,000

65,000

45,000

40,000

x

y

z

Invest $65,000 in the Potus Fund

Invest $45,000 in the Stong Fund

Invest $40,000 in the Franklin Fund

-1 R2 + R1 R12R2 + R3 R3

0 1 1.5 105,000

1 1 1 150,000

1 0 0.5 45,000

1 0 0.5 45,000

0 1 1.5 105,000

0 0 1 40,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

2009 PBLPathways

0.5 R3 + R1 R1-1.5 R3 + R2 R2

2 2 4 6

2 3 1 1

0 1 3 5

1 0 0 65,000

0 1 0 45,000

0 0 1 40,000

65,000

45,000

40,000

x

y

z

Invest $65,000 in the Potus Fund

Invest $45,000 in the Stong Fund

Invest $40,000 in the Franklin Fund

-1 R2 + R1 R12R2 + R3 R3

0 2 3 210,000

0 2 2 170,000

0 0 1 40,000

1 0 0.5 45,000

0 1 1.5 105,000

0 0 1 40,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

2009 PBLPathways

0.5 R3 + R1 R1-1.5 R3 + R2 R2

2 2 4 6

2 3 1 1

0 1 3 5

1 0 0 65,000

0 1 0 45,000

0 0 1 40,000

65,000

45,000

40,000

x

y

z

Invest $65,000 in the Potus Fund

Invest $45,000 in the Stong Fund

Invest $40,000 in the Franklin Fund

-1 R2 + R1 R12R2 + R3 R3

0 2 3 210,000

0 2 2 170,000

0 0 1 40,000

1 0 0.5 45,000

0 1 1.5 105,000

0 0 1 40,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

2009 PBLPathways

0.5 R3 + R1 R1-1.5 R3 + R2 R2

2 2 4 6

2 3 1 1

0 1 3 5

1 0 0 65,000

0 1 0 45,000

0 0 1 40,000

65,000

45,000

40,000

x

y

z

Invest $65,000 in the Potus Fund

Invest $45,000 in the Stong Fund

Invest $40,000 in the Franklin Fund

-1 R2 + R1 R12R2 + R3 R3

0 2 3 210,000

0 2 2 170,000

0 0 1 40,000

1 0 0.5 45,000

0 1 1.5 105,000

0 0 1 40,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

2009 PBLPathways

0.5 R3 + R1 R1-1.5 R3 + R2 R2

0 0 0.5 20,000

1 0 0.5 45,000

1 0 0 65,000

1 0 0 65,000

0 1 0 45,000

0 0 1 40,000

65,000

45,000

40,000

x

y

z

Invest $65,000 in the Potus Fund

Invest $45,000 in the Stong Fund

Invest $40,000 in the Franklin Fund

-1 R2 + R1 R12R2 + R3 R3

0 2 3 210,000

0 2 2 170,000

0 0 1 40,000

1 0 0.5 45,000

0 1 1.5 105,000

0 0 1 40,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

2009 PBLPathways

0.5 R3 + R1 R1-1.5 R3 + R2 R2

0 0 0.5 20,000

1 0 0.5 45,000

1 0 0 65,000

1 0 0 65,000

0 1 0 45,000

0 0 1 40,000

65,000

45,000

40,000

x

y

z

Invest $65,000 in the Potus Fund

Invest $45,000 in the Stong Fund

Invest $40,000 in the Franklin Fund

-1 R2 + R1 R12R2 + R3 R3

0 2 3 210,000

0 2 2 170,000

0 0 1 40,000

1 0 0.5 45,000

0 1 1.5 105,000

0 0 1 40,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

2009 PBLPathways

0.5 R3 + R1 R1-1.5 R3 + R2 R2 1 0 0 65,000

0 1 0 45,000

0 0 1 40,000

65,000

45,000

40,000

x

y

z

Invest $65,000 in the Potus Fund

Invest $45,000 in the Stong Fund

Invest $40,000 in the Franklin Fund

-1 R2 + R1 R12R2 + R3 R3

0 2 3 210,000

0 2 2 170,000

0 0 1 40,000

1 0 0.5 45,000

0 1 1.5 105,000

0 0 1 40,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

0 0 1.5 60,000

0 1 1.5 105,000

0 1 0 45,000

2009 PBLPathways

0.5 R3 + R1 R1-1.5 R3 + R2 R2

0 0 1.5 60,000

0 1 1.5 105,000

0 1 0 45,000

1 0 0 65,000

0 1 0 45,000

0 0 1 40,000

65,000

45,000

40,000

x

y

z

Invest $65,000 in the Potus Fund

Invest $45,000 in the Stong Fund

Invest $40,000 in the Franklin Fund

-1 R2 + R1 R12R2 + R3 R3

0 2 3 210,000

0 2 2 170,000

0 0 1 40,000

1 0 0.5 45,000

0 1 1.5 105,000

0 0 1 40,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

2009 PBLPathways

0.5 R3 + R1 R1-1.5 R3 + R2 R2

0 0 1.5 60,000

0 1 1.5 105,000

0 1 0 45,000

1 0 0 65,000

0 1 0 45,000

0 0 1 40,000

65,000

45,000

40,000

x

y

z

Invest $65,000 in the Potus Fund

Invest $45,000 in the Stong Fund

Invest $40,000 in the Franklin Fund

-1 R2 + R1 R12R2 + R3 R3

0 2 3 210,000

0 2 2 170,000

0 0 1 40,000

1 0 0.5 45,000

0 1 1.5 105,000

0 0 1 40,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000

2009 PBLPathways

0.5 R3 + R1 R1-1.5 R3 + R2 R2

0 0 1.5 60,000

0 1 1.5 105,000

0 1 0 45,000

1 0 0 65,000

0 1 0 45,000

0 0 1 40,000

65,000

45,000

40,000

x

y

z

Invest $65,000 in the Potus Fund

Invest $45,000 in the Stong Fund

Invest $40,000 in the Franklin Fund

-1 R2 + R1 R12R2 + R3 R3

0 2 3 210,000

0 2 2 170,000

0 0 1 40,000

1 0 0.5 45,000

0 1 1.5 105,000

0 0 1 40,000

1 1 1 150,000

0 1 1.5 105,000

0 2 2 170,000