SOLUTION: A man invests a total of $21,000 in two accounts, one paying 5.5% simple interest per year and the other paying 8.5% simple interest per year. His annual interest from both account
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Question 595327: A man invests a total of $21,000 in two accounts, one paying 5.5% simple interest per year and the other paying 8.5% simple interest per year. His annual interest from both account is $1,280. How much did he invest at each rate? Answer by math-vortex(648) (Show Source):
You can put this solution on YOUR website! [I] Define the variables.
x = the amount invested in the first account
y = the amount invested in the second account
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[II] Write a system of equations.
The total amount invested in the two accounts is x + y, so
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The first account pays 5.5% simple interest per year on the amount invested in that account. An algebraic expression for this quantity is 0.055x. (I wrote 5.5% as a decimal.)
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The second account pays 8.5% simple interest per year on the amount invested in that account. An algebraic expression for this quantity is 0.085y.
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The annual interest (per year) for both accounts, $1280 is the sum of the interest from the first account and the second account combined, so
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[III] Solve the system of equations for x and y.
The substitution method looks like an efficient method to solve this.
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Rewrite the first equation.
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Substitute 21500-x for y in the second equation.
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Simplify and solve for x.
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Substitute the value of x back into the first equation.
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[III] Check your solution in the second equation.
Check!
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The man invested $18,250 in the 5.5% account and $3,250 in the 8.5% account.
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Hope this helps! Feel free to email if you have questions about this problem.
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Mrs.Figgy
math.in.the.vortex@gmail.com
