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Jack invests $1000 at a certain annual interest rate, and he invests another $2000 at an annual rate that is one-half percent higher. If he receives a total of $160 interest in 1 year, at what rate is the $1000 invested?

 Sep 26, 2014

Best Answer 

 #1
avatar+17746 
+5

Since 1 percent is 0.01, one-half percent is 0.005.

Let x be the interest rate of the $1000 investment; then x + 0.005 will be the interest rate of the $2000 investment.

Formula: (Amount Invested)(Interest Rate) + (Amount Invested)(Interest Rate) = (Interest Earned) 

     (1000)(x) + (2000)(x+0.005) = 160

     1000x + 2000x + 10 = 160

      3000x + 10 = 160

      3000x = 150

      x = 150 / 3000

      x = 0.05    ---> The $1000 is invested at 5%.

Check: ($1000)(0.05) + ($2000)(0.055) = $50 + $110 = $160

 Sep 26, 2014
 #1
avatar+17746 
+5
Best Answer

Since 1 percent is 0.01, one-half percent is 0.005.

Let x be the interest rate of the $1000 investment; then x + 0.005 will be the interest rate of the $2000 investment.

Formula: (Amount Invested)(Interest Rate) + (Amount Invested)(Interest Rate) = (Interest Earned) 

     (1000)(x) + (2000)(x+0.005) = 160

     1000x + 2000x + 10 = 160

      3000x + 10 = 160

      3000x = 150

      x = 150 / 3000

      x = 0.05    ---> The $1000 is invested at 5%.

Check: ($1000)(0.05) + ($2000)(0.055) = $50 + $110 = $160

geno3141 Sep 26, 2014

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