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

Grace Cathey

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Dec 18, 2018
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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.

PrincipleRateInterest
x.09x/3(.0575)+ $425
x/3.0575x/3(.0575)

Now what do I do? I know that I am probably missing something SUPER simple...:D;)
 

tkhunny

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Apr 12, 2005
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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...:D;)
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

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Dec 30, 2014
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3,045
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.

PrincipleRateInterest
x.09x(.09)
x/3.0575x/3(.0575)+ $425

Now what do I do? I know that I am probably missing something SUPER simple...:D;)
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

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Dec 18, 2018
Messages
5
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
Joined
Dec 18, 2018
Messages
5
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"?
 
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