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

[Grace Cathey]

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]

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.

 

[Steven G]

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]

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"?