Scott and Laura have both invested some money. Scott invested $2500 more than Laura and at a 3% higher interest rate. If Scott received $900 annual interest and Laura received $450, how much did Scott invest?
s(1+r) = 900
(s-2500)*(1+r-.03) = 450
I get s=10,000, but a negative interest rate. Is there a typo?
no, I copied the question just as it is, there is 2 answers, the $10,000 is the smaller amount he invested, there should also be a larger amount.
To find out how much Scott invested, let's assume that Laura invested "x" dollars.
According to the information given, Scott invested $2500 more than Laura. So, Scott's investment is x + $2500.
The interest rate on Laura's investment is given as 3% less than Scott's interest rate. Let's assume the interest rate on Laura's investment is "r%". Therefore, the interest rate on Scott's investment is (r+3)%.
Now, we can use the formula for simple interest to determine how much interest each person received. The formula is:
Interest = Principal * Rate * Time
For Laura:
Interest = Laura's investment * Laura's interest rate * 1 year
450 = x * r% * 1
For Scott:
Interest = Scott's investment * Scott's interest rate * 1 year
900 = (x + $2500) * (r+3)% * 1
Now, we can solve these two equations to find the values of "x" and "r".
From the first equation, we get:
450 = x * r%
Divide both sides by "x":
450/x = r%
From the second equation, we get:
900 = (x + $2500) * (r+3)%
Divide both sides by (x + $2500):
900 / (x + $2500) = (r+3)%
Now we have two equations:
450/x = r% --(1)
900 / (x + $2500) = (r+3)% --(2)
To eliminate the percentages, divide both sides of equation (1) by 100:
4.5/x = r --(3)
Now we can substitute equation (3) into equation (2):
900 / (x + $2500) = (4.5/x +3)
To avoid dealing with fractions, cross-multiply:
900 * x = (4.5/x +3) * (x + $2500)
Expand the right side:
900x = 4.5 + 3x + $7500
Subtract 3x from both sides:
900x - 3x = 4.5 + $7500
Combine like terms:
897x = 4.5 + $7500
Convert the dollars to cents:
897x = 450 + 750000
897x = 750450
Divide both sides by 897 to solve for x:
x = 750450 / 897 ≈ 836.57
So, Laura invested approximately $836.57.
Now, we can find Scott's investment:
Scott's investment = Laura's investment + $2500
= $836.57 + $2500
≈ $3336.57
Therefore, Scott invested approximately $3336.57.