Question

An investor invested 1.1 million dollars into two land investments. On the first investment, Swan Peak, her return was a 110% increase on the money she invested. On the second investment, Riverside Community, she earned 50% over what she invested. If she earned $1 million in profits, how much did she invest in each of the land deals?

Answer 1

The investor invested $0.75 million in Swan Peak and $0.35 million in Riverside Community. She earned $1 million in profits, with a 110% return on Swan Peak and a 50% return on Riverside Community.

Let's denote the amount invested in Swan Peak as S and the amount invested in Riverside Community as R. The problem states that the total investment is $1.1 million.

So, S + R = 1.1 million dollars.

The investor earned a 110% return on Swan Peak, which means she made a profit of 110% of the amount invested in Swan Peak:

`\[ \text{Profit from Swan Peak} = 1.1S \]`

She earned a 50% return on Riverside Community, which means she made a profit of 50% of the amount invested in Riverside Community:

`\[ \text{Profit from Riverside Community} = 0.5R \]`

The total profit is given as $1 million:

`\[ \text{Total Profit} = \text{Profit from Swan Peak} + \text{Profit from Riverside Community} \]\[ 1 \text{ million} = 1.1S + 0.5R \]`

Now, we can use the first equation to express one variable in terms of the other. Let's solve for S:

S = 1.1 - R

Now, substitute this expression for S into the profit equation:

`\[ 1 \text{ million} = 1.1(1.1 - R) + 0.5R \]`

Simplify and solve for R :

`\[ 1 \text{ million} = 1.21 - 1.1R + 0.5R \]`

Combine like terms:

`\[ 1 \text{ million} = 1.21 - 0.6R \]`

Subtract 1.21 from both sides:

-0.21 = -0.6R

Divide by -0.6:

`\[ R = (0.21)/(0.6) \]`

R = 0.35

Now that we have the value for R, we can substitute it back into the first equation to find S :

S + 0.35 = 1.1

S = 1.1 - 0.35

S = 0.75

So, the investor invested $0.75 million in Swan Peak and $0.35 million in Riverside Community.