Rational Equations

Question

Octavian invests some money at 8.5% and half as much at 10%. in time, he receives $1000 interest. how much did he invest at each rate?

Answer 1

One way to do this problem is to make a table with the first investment in the first row and the second in the second row. We'll call the first investment's initial amount x, and the second investment's initial amount 0.5x (since it's half as much). The interest for each investment will be the initial amount times the interest rate.

 

 

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|  INITIAL AMOUNT  |  INTEREST RATE  |        INTEREST       |

|------------------------------------------------------------------------------------

|               x               |             0.085          |           0.085x         |

|------------------------------------------------------------------------------------

|             0.5x            |               0.1            |        0.1(0.5x)        |

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The problem tells us that, at some point, Octavian receives $1000 interest. Knowing the interest he got from each investment, we can set up an equation and solve for x:

 

0.085x + 0.1(0.5x) = $1000

0.085x + 0.05x = $1000

0.135x = $1000

x = $7,407.41

 

Remember, x was for the first investment. So, he invested $7,407.41 at 8.5% and $3,703.70 (half that) at 10%.