# Investment Word Problem: Tom invests sum at 9%, and 1/3 of sum at 5.75%

#### Grace Cathey

##### New member
Tom has a sum of money invested at 9% and another sum that is 1/3 of the first sum invested at 5 3/4%. The yearly income from the 9% investment exceeds the interest of the 5 3/4% investment by $425. How much is invested at each rate? I can get all of my information organized like this: (I left out time since it is a year and won't make a difference.  Principle Rate Interest x .09 x/3(.0575)+$425 x/3 .0575 x/3(.0575)

Now what do I do? I know that I am probably missing something SUPER simple...

#### tkhunny

##### Moderator
Staff member
Tom has a sum of money invested at 9% and another sum that is 1/3 of the first sum invested at 5 3/4%. The yearly income from the 9% investment exceeds the interest of the 5 3/4% investment by $425. How much is invested at each rate? I can get all of my information organized like this: (I left out time since it is a year and won't make a difference.  Principle Rate Interest x .09 x/3(.0575)+$425 x/3 .0575 x/3(.0575)

Now what do I do? I know that I am probably missing something SUPER simple...
I think you have it. You just substituted the 9% interest too soon and became confused. Write out the entire table before you start substituting.

x * 0.09 = (x/3)(.0575) + $425 -- Additional parentheses are not necessary, but they do reduce possible confusion. #### Jomo ##### Elite Member Tom has a sum of money invested at 9% and another sum that is 1/3 of the first sum invested at 5 3/4%. The yearly income from the 9% investment exceeds the interest of the 5 3/4% investment by$425. How much is invested at each rate?

I can get all of my information organized like this:
(I left out time since it is a year and won't make a difference.

 Principle Rate Interest x .09 x(.09) x/3 .0575 x/3(.0575)+ $425 Now what do I do? I know that I am probably missing something SUPER simple... Since the interest from the 9% is more that the interest from the 5.75% you need to add the$425 to the interest from the 5.75% to make them equal.

#### Grace Cathey

Since the interest from the 9% is more that the interest from the 5.75% you need to add the $425 to the interest from the 5.75% to make them equal. Thank you!!!! #### Grace Cathey ##### New member Since the interest from the 9% is more that the interest from the 5.75% you need to add the$425 to the interest from the 5.75% to make them equal.
Are you talking about the "golden rule of equations"?