Word Problem

Question

An actor invested some money at 5% simple interest, and $29,000 more than twice the amount at 6%. The total annual interest earned from the investment was $11,770. How much did he invest at each amount?

Answer 1

I = prt

 

11770 = p(.05)(1) + (2p + 29000)(.06)(1)

 

11770 = .05p + 0.12p + 1740

10030 = 0.17p

p = $59,000 at 5%

 

2p + 29000 = 147,000 at 6%

 

Check:  .05(59000) + .06(2(59000)+29000) = $11,770 interest

Answer 2

X is the amount invested at 5%

 

5% of X + 6% of (2x + 29000) = 11770

 

0.05X + 0.06(2X + 29000) = 11770

 

5X + 6(2x + 29000) = 1177000 <-- multiplies everything by 100 to clear away the decimals

 

5X + 12X + 174000 = 1177000

 

17X = 1003000

 

X=59000

 

So $59,000 invested at 5% AND

 2(59000) + 29000 = $147,000 invested at 6%

 

The return is 5% of $59,000 + 6% of $147,000 =

                 0.05*59000 + 0.06*147000 = 2950 + 8820 = $11,770.

 So the answers in bold above are correct