You invested $4000, part at 5% and the remainder at 9% annual interest. At the end of the year, the total interest from these investments was $311. How much was invested at each rate?
Let the part invested at
So we can write
Multiplying both sides of
So plugging the value
Improved my method by cutting out s step.
$2775 was invested at 9%
$1225 was invested at 5%
Suppose all the money was invested at 5% then the income would be
Suppose all the money was invested at 9% then the income would be
Consider this transition of total interest received by varying the amount deposited in each account.
This can be modelled by modelling just one account. If all of the money is in the 9% account then none is in the 5% account. If all the money is in the 5% account then there is none in the 9% account. So one account infers directly how much is in the other as the funds available is fixed at $4000
The result is a straight line graph where the gradient is the change in interest depending on how much is in each account.
The equation of this graph will be:
We are told that the target interest is $311.
Dropping the $ sign for now
Subtract 200 from both sides
Multiply both sides by 25
Thus the amount of the principle sum in the 5% account is: