scott and laura have both invested some money. Scott invested $3,000 more then laura and at a 2% higher interest rate. If scott received $800 annual interest and laura received $400, how much did scott invest?

Let their investments be L (Laura) and S (Scott). Laura's annual interest rate is I (expressed as a decimal) and Scott's is I + 0.02

S = L + 3000
800 = S*(I + 0.02)
400 = L I
You have three equations in three unknowns, which is enough to solve for all of them.
800 =(L+300)(I+0.02)
800 = LI + 300I +0.02L + 6
= 400 + 300I + 0.02L+ 6
= 400 + 300*400/L + 0.02L + 6
= 406 + 120000/L +0.02L
This can be turned into a quadratic equation for L. Take the positive root.

Actually, you should take the negative root. You should plug both answers into the original equation to see which one fits. The one that makes sense (i.e. 800=800) should be the correct one.

Don't forget that Scott invested 3,000 more than Sally (S = L + 3000). You just solved for L. The question is asking for what S is. You're not done yet.

Let's assume that Laura's investment amount is "x" dollars.

According to the given information, Scott has invested $3,000 more than Laura. So, Scott's investment amount can be represented as "x + $3,000".

Furthermore, Scott's investment has a 2% higher interest rate than Laura's investment.

The annual interest Scott received is $800, and Laura received $400. Let's calculate the interest rates for both of them:

Scott's interest rate: $800 / Scott's investment amount
Laura's interest rate: $400 / Laura's investment amount

Since Scott's interest rate is 2% higher than Laura's interest rate, we can set up the following equation:

Scott's interest rate = Laura's interest rate + 2%

$800 / (x + $3,000) = $400 / x + 2%

To solve this equation, we can cross-multiply:

($800 * x + $800 * 2%) = ($400 * (x + $3,000))

Expanding the equation:

$800x + $16 + $800x = $400x + $1,200 * $400

Combining like terms:

$1,600x + $16 = $400x + $1,200

Moving the variables to one side and the constants to the other side:

$1,600x - $400x = $1,200 - $16

Simplifying:

$1,200x = $1,184

Now, we can solve for "x" by dividing both sides of the equation by $1,200:

x = $1,184 / $1,200

Calculating "x":

x ≈ 0.9866

Since "x" represents Laura's investment amount, we can conclude that Scott's investment amount is:

Scott's investment amount = Laura's investment amount + $3,000

Scott's investment amount ≈ 0.9866 + $3,000 ≈ $3,986.60

Therefore, Scott invested approximately $3,986.60.

To find out how much Scott invested, we can solve this problem step by step:

Let's assume that Laura invested x dollars.
Since Scott invested $3,000 more than Laura, he invested (x + 3000) dollars.

We also know that Scott's interest rate is 2% higher than Laura's interest rate. Let's assume Laura's interest rate is y%. So, Scott's interest rate is (y + 2)%.

To calculate the interest earned by each person, we can use the formula: (amount invested) × (interest rate) = (annual interest earned).

For Laura, we have:
x × (y/100) = 400

For Scott, we have:
(x + 3000) × (y + 2)/100 = 800

Now, we have two equations with two variables. We can solve this system of equations to find the values of x and y.

Simplifying the first equation:
xy/100 = 400
xy = 400 × 100
xy = 40,000

Simplifying the second equation:
((x + 3000) × (y + 2))/100 = 800
(x + 3000) × (y + 2) = 800 × 100
(x + 3000) × (y + 2) = 80,000

Expanding the equation:
xy + 2x + 3000y + 6000 = 80,000

Now we can substitute the value of xy we found earlier:
40,000 + 2x + 3000y + 6000 = 80,000

Combining like terms:
2x + 3000y + 46,000 = 80,000

Rearranging terms:
2x + 3000y = 80,000 - 46,000
2x + 3000y = 34,000

Now, we can solve this equation using the given information.

From here, we would need another piece of information to solve for the values of x and y, such as the value of either x or y or a relationship between them.