Problema Solution
Eva invested a certain amount of money at 8% interest and $1500 more than that amount at 9%. Her total yearly interest was $645. How much did she invest at each rate?
Answer provided by our tutors
We assume the money earned is based on simple interest, which can be expressed as "prt". Let 'p' represent the princial amount, 'r' represent the decimal of the rate (9% is 0.09), and 't' represents the number of years, which is equal to '1' in this problem.
The problem statement is the sum of interest earned based on two different interest rates and two different principal amounts. Let 'x' represent the amount of money earcned at 8%, then 'x+1500' represents the amount of money earched at 9%. The total amount earned was $645:
645 = x0.08 + (x+1500)0.09
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x=3000
3000+1500=4500
So $3,000 was invested at 8% and $4,500 was invested at 9%.