SOLUTION: How can $6300 be invested, one part at 4% p.a. and the remainder at 5% p.a., so that the simple interest will be the same on each investment? Thanks for helping me!

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Question 189687: How can $6300 be invested, one part at 4% p.a. and the remainder at 5% p.a., so that the simple interest will be the same on each investment?
Thanks for helping me!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let
x = amount invested at 4%
y = amount invested at 5%



Since $6,300 is invested, this means that x%2By=6300. Solve for "y" to get y=6300-x


Also, because we want the simple interest in both investments to be equal, this means that 0.04x=0.05y. Multiply both sides by 100 to get 4x=5y


4x=5y Start with the second equation.


4x=5%286300-x%29 Plug in y=6300-x


4x=31500-5x Distribute.


4x%2B5x=31500 Add 5x to both sides.


9x=31500 Combine like terms on the left side.


x=%2831500%29%2F%289%29 Divide both sides by 9 to isolate x.


x=3500 Reduce.


So $3,500 needs to be invested at 4%


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y=6300-x Go back to the first equation


y=6300-3500 Plug in x=3500


y=2800 Combine like terms.


So $2,800 is needed to be invested at 5%