1. ## Help on an investment prob. pleasee

Hey guys new to this forum, and not real good with math. But i really like it, and hope to get better as time goes on

But heres the problem: A broker invested $24,000 in two mutual funds, one earning 9% annual interest and the other earning 14%. After 1 year, his combined interest is$3,135. How much was invested at each rate?

Can anyone give me a nice forumula i can use for this prob., including an answer? thankyou so much!!

2. Hello, Baginoman!

Welcome aboard!

There is no nice formula for this,
. . but we can think our way through it.

A broker invested $24,000 in two mutual funds, one earning 9% annual interest and the other earning 14%. After 1 year, his combined interest is$3,135.
How much was invested at each rate?

Let $x$ = amount invested at 9%.
Then $24,000 - x$ = amount invested at 14%.

He invested $x$ dollars at 9%.
. . The interest is: . $0.09x$ dollars.

He invested $24,000 - x$ dollars at 14%.
. . The interest is: . $0.14(24,000-x)$ dollars.

Hence, his total interest is: . $0.09x + 0.14(24,000 - x)$ dollars.

But we are told that his total interest is $\3,135$.

There is our equation! . . . $0.09x + 0.14(24,000-x) \;=\;3135$

Got it?

3. well i kinda got the same forumula, but the wrong answer from the book? haha

so if its: .09x + 3,360 - .14x = 3,135(subtracting .09 from both sides)=>

3,360 - .23x = 3135(Subtracting 3,360 to the other side)=>

-23x = .225(divide)= $978? I get totally diff answer from the book 4. Originally Posted by Baginoman well i kinda got the same forumula, but the wrong answer from the book? haha so if its: .09x + 3,360 - .14x = 3,135(subtracting .09 from both sides)=> 3,360 - .23x = 3135(Subtracting 3,360 to the other side)=> -23x = .225(divide)=$978?

I get totally diff answer from the book
Your first step above is incorrect - you don't need to subtract .09x from both sides, becuase there is no .09x on the right had side. Start out by combining like terms:

.09x + 3,360 -.14x = 3,135
(.09x-.14x) = 3135-3360
-.05x = -225
x = 4,500.

Some advice: always double check your answers. In your case when you got x = 978, if you plug that back into the original equation you would have:

.09*978 + 3,360 -.14*978 = 3,135
88+3,360-137 = 3,135
3,311 = 3,135

Clearly something is not right with x= 978, so you would know to go back and look for an error in your work. Hope this helps.