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Question 543115: Amanda invests $25,000, part at 5% and the rest at 6%. The annual return on the 5% investment exceeds the annual return on the 6% investment by $40. How much did she invest at each rate?
I know that I have to form an formula, but I'm not sure how. We didn't go over this in class. : (
Answer by jpg7n16(66)   (Show Source):
You can put this solution on YOUR website! Take it slow, and start turning the phrases into equations:
"Amanda invests $25,000, part at 5% and the rest at 6%."
Sooo what does that mean? It means she invests some amount (let's say A) and some other amount (let's say B) that total $25,000. What is the simplest formula you can make from this?
"The annual return on the 5% investment"
Okay so now we know that one of our investments (either A or B) makes 5% for every dollar invested. How do you express this as an equation? Well each dollar of let's say A makes 5% or $0.05.
"exceeds the annual return on the 6% investment by $40.}}}
Here we have 2 pieces of information. Piece one: our second investment (B) makes 6%. We know what to do with that.
But now we know that it 'exceeds' the return by $40. What does that mean? It means when you take a 5% return on A and subtract a 6% return on B, you'll still have $40. As an equation:
And now we have our two formulas which we'll be able to "stack" and solve this problem:
1)
2)
.
To make this easier to read, let's get rid of those decimals. Multiply line 2 by 100.
1)
2) 
Much better. Now we need to make the equations have the same number of A's or B's so that we can cancel them out. Since one of the B's is already negative, let's make each equation have 6 B's. Multiply #1 by 6.
1) 
2)
Now just add them together and the B's will cancel out!
divide by 11
.
Now comes the easy part. Just find the easier equation of our original equations, and plug back in $14,000 for A. And I think you'll agree, equation 1 is MUCH easier:
1)
.
"How much did she invest at each rate?"
A is our 5% investment, so $14,000 @ 5%
B is our 6% investment, so $11,000 @ 6%
.
Remember these steps and you'll do fine. Hope this helps!
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