SOLUTION: Phyllis invested $12,500, a portion earning a simple interest rate of 3.5% per year and the rest earning a rate of 3% per year. After one year the total interest earned on these

Question 902461: Phyllis invested $12,500, a portion earning a simple interest rate of 3.5%
per year and the rest earning a rate of 3% per year. After one year the total interest earned on these investments was $420.00. How much money did she invest at each rate?
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
We know the total amount of money invested. $12500
x+y=12500,
We know that the total interest for the year for the two accounts is $420
0.035*x+0.03*y=420
x=12500-y
We substitute for x
0.035*(12500-y)+0.03*y=420
We multiply out
437.5-0.035y+0.03*y=420
We combine like terms.
-0.005*y=-17.5
Isolate y
y=3500 at 3%
x=12500-y
Calculate x
x=9000 at 3.5%
We check
0.035*9000+0.03*3500=420
315.0+105=420
420.0=420

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