1. ## AlgebraII Word Problem-Help

John was injured on the job and receievd a setllement of $1.5 million that he can live on for his retirement. John is going to pay off his debts(including his house) of$550,000. He is going to invest the balance in two accounts. One pays 7.5% and the other 4.5%. John will ONLY need $58,500 in order to live ar his current level. a. Write a system of equations that will help you determine the amount to be invested in each account. b. How much should John invest in each account in order to earn the$58,500 he needs?

2. couple of assumptions here since they were not in the problem statement ...
1. interest is simple interest per annum
2. he needs $58,500 per year to support his present lifestyle$1.5 million - $550,000 =$950,000

let x = amount of money invested at 7.5% interest
then (950,000 - x) = amount of money invested at 4.5% interest

interest earned = 58,500 = (x)(7.5%) + (950,000 - x)(4.5%)

don't forget to change the percentages to decimals ... then solve for x.

3. Originally Posted by ep78
John was injured on the job and receievd a setllement of $1.5 million that he can live on for his retirement. John is going to pay off his debts(including his house) of$550,000. He is going to invest the balance in two accounts. One pays 7.5% and the other 4.5%. John will ONLY need $58,500 in order to live ar his current level. a. Write a system of equations that will help you determine the amount to be invested in each account. b. How much should John invest in each account in order to earn the$58,500 he needs?
Using a system of equations, it would look like this:

Let x = amount invested at 7.5%
Let y = amount invested at 4.5%
Let $950,000 = total investment Let$58,500 = interest needed
_____________________________
$\displaystyle x+y=950000$

$\displaystyle .075x+.045y=58500$
_____________________________

Solve the system