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Client Investments. A & B Financial Services makes investments for their clients. It makes a investment of $3700 for the year at simple interest, yielding $297. some of the dollars is invested at 7% and the rest at 9%. How much has been invested at 7% and 9 %? Do the Familiarize and Translate steps by completing the following table. Let the number of money invested at 7% and the number of money invested at 9%.

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  1. Let x be the amount (in dollars) invested at 7%, and let y be the amount (in dollars) invested at 9%. The sum of the investments is $3700, so x + y = 3700 The interest made on x dollars at 7% is 0.07x The interest made on y dollars at 9% is 0.09y So the total interest made is 0.07x + 0.09y. You are told that this amount is $297. So 0.07x + 0.09y = 297 So you need to solve the system x + y = 3700 0.07x + 0.09y = 297 Solve the first equation for, say, x in terms of y: x = 3700 - y Now use this to substitute for x in the other equation: 0.07(3700 - y) + 0.09y = 297 259 - 0.07y + 0.09y = 297 259 + 0.02y = 297 0.02y = 38 y = 38/0.02 = 1900 x = 3700 - y = 3700 - 1900 = 1800 $1800 has been invested at 7% and $1900 has been invested at 9%.
  2. I would suggest to solve this with 2 equations in 2 unknowns. We can make these 2 equations from 2 pieces of information: total money and total interest. Let's give some names to this money: X = the amount of money invested at 7% Y = the amount of money invested at 9% We get the first equation from knowing the total amount of money, so X+Y=3700 We get the second equation from knowing the total amount of interest, so .07X + .09Y = 297 This gives us 2 equations in 2 unknowns. I would solve this by substitution: solve the first equation for X and substitute into the second equation. X = 3700-Y .07(3700-Y) + .09 = 297 259 + .02Y = 297 .02Y = 38 Y = 1900 X = 3700 - 1900 = 1800 We can also find how the $297 in interest earned splits between the two funds X and Y The one that earns 7%: .07*1800=171 The one that earns 9%: .09*1900=126 171 + 126 = 297 total interest earned
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