Math / Algebra

QuestionDevon invested $\$ 8500$ in three different mutual funds. A fund containing large cap stocks made $7.3 \%$ return in 1 yr. A real estate fund lost $13.2 \%$ in 1 yr, and a bond fund made $5.4 \%$ in 1 yr . The amount invested in the large cap stock fund was twice the amount invested in the real estate fund. If Devon had a net return of $\$ 163$ across all investments, how much was invested in each fund?

Studdy Solution

STEP 1

1. Devon invested a total of \$8500 in three mutual funds.
2. The large cap stock fund made a 7.3% return.
3. The real estate fund lost 13.2%.
4. The bond fund made a 5.4% return.
5. The amount invested in the large cap stock fund was twice the amount invested in the real estate fund.
6. Devon had a net return of \$163 from all investments.

STEP 2

1. Define variables for the amounts invested in each fund.
2. Set up equations based on the problem's conditions.
3. Solve the system of equations to find the amounts invested in each fund.

STEP 3

Define variables for the amounts invested in each fund.
Let $x$ be the amount invested in the real estate fund. Let $2x$ be the amount invested in the large cap stock fund. Let $y$ be the amount invested in the bond fund.

STEP 4

Set up equations based on the problem's conditions.
Equation 1: Total investment equation $x + 2x + y = 8500$
Equation 2: Net return equation $0.073(2x) - 0.132x + 0.054y = 163$

STEP 5

Simplify and solve the system of equations.
From Equation 1: $3x + y = 8500$
Substitute $y = 8500 - 3x$ into Equation 2: $0.073(2x) - 0.132x + 0.054(8500 - 3x) = 163$
Simplify: $0.146x - 0.132x + 459 - 0.162x = 163$ $-0.148x + 459 = 163$

STEP 6

Continue solving for $x$ .
Subtract 459 from both sides: $-0.148x = 163 - 459$ $-0.148x = -296$
Divide by -0.148: $x = \frac{-296}{-0.148}$ $x = 2000$

STEP 7

Find the amounts for the other funds.
Since $x = 2000$ , the amount invested in the real estate fund is \$2000.
The amount invested in the large cap stock fund is $2x = 2(2000) = 4000$ .
Substitute $x = 2000$ into $y = 8500 - 3x$ : $y = 8500 - 3(2000)$ $y = 8500 - 6000$ $y = 2500$
The amounts invested in each fund are: - Real estate fund: \$2000 - Large cap stock fund: \$4000 - Bond fund: \$2500

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Studdy Solution

STEP 1

STEP 2

1. Define variables for the amounts invested in each fund.
2. Set up equations based on the problem's conditions.
3. Solve the system of equations to find the amounts invested in each fund.

STEP 3

Define variables for the amounts invested in each fund.
Let $x$ be the amount invested in the real estate fund. Let $2x$ be the amount invested in the large cap stock fund. Let $y$ be the amount invested in the bond fund.

STEP 4

Set up equations based on the problem's conditions.
Equation 1: Total investment equation $x + 2x + y = 8500$
Equation 2: Net return equation $0.073(2x) - 0.132x + 0.054y = 163$

STEP 5

Simplify and solve the system of equations.
From Equation 1: $3x + y = 8500$
Substitute $y = 8500 - 3x$ into Equation 2: $0.073(2x) - 0.132x + 0.054(8500 - 3x) = 163$
Simplify: $0.146x - 0.132x + 459 - 0.162x = 163$ $-0.148x + 459 = 163$

STEP 6

Continue solving for $x$ .
Subtract 459 from both sides: $-0.148x = 163 - 459$ $-0.148x = -296$
Divide by -0.148: $x = \frac{-296}{-0.148}$ $x = 2000$

STEP 7

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Studdy Solution

STEP 1

STEP 2

1. Define variables for the amounts invested in each fund.2. Set up equations based on the problem's conditions.3. Solve the system of equations to find the amounts invested in each fund.

STEP 3

Define variables for the amounts invested in each fund.Let x x x be the amount invested in the real estate fund. Let 2x 2x 2x be the amount invested in the large cap stock fund. Let y y y be the amount invested in the bond fund.

STEP 4

Set up equations based on the problem's conditions.Equation 1: Total investment equation x+2x+y=8500 x + 2x + y = 8500 x+2x+y=8500Equation 2: Net return equation 0.073(2x)−0.132x+0.054y=163 0.073(2x) - 0.132x + 0.054y = 163 0.073(2x)−0.132x+0.054y=163

STEP 5

STEP 6

Continue solving for x x x.Subtract 459 from both sides: −0.148x=163−459 -0.148x = 163 - 459 −0.148x=163−459 −0.148x=−296 -0.148x = -296 −0.148x=−296Divide by -0.148: x=−296−0.148 x = \frac{-296}{-0.148} x=−0.148−296​ x=2000 x = 2000 x=2000

STEP 7

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Define variables for the amounts invested in each fund.
2. Set up equations based on the problem's conditions.
3. Solve the system of equations to find the amounts invested in each fund.

Define variables for the amounts invested in each fund.
Let $x$ be the amount invested in the real estate fund. Let $2x$ be the amount invested in the large cap stock fund. Let $y$ be the amount invested in the bond fund.

Set up equations based on the problem's conditions.
Equation 1: Total investment equation $x + 2x + y = 8500$
Equation 2: Net return equation $0.073(2x) - 0.132x + 0.054y = 163$

Continue solving for $x$ .
Subtract 459 from both sides: $-0.148x = 163 - 459$ $-0.148x = -296$
Divide by -0.148: $x = \frac{-296}{-0.148}$ $x = 2000$