SOLUTION: Reggie Means invested part of $30,000 in municipal bonds that earn 6.5% annual simple interest and the remainder of the money in 8.5% corporate bonds. How much is invested in each

Question 541390: Reggie Means invested part of $30,000 in municipal bonds that earn 6.5% annual simple interest and the remainder of the money in 8.5% corporate bonds. How much is invested in each account if the total annual interest earned is $2190?

The rest of my homework has questions similar to this one, but for some reason I can't find a formula that works! If you could help me find one, I should be able to finish the rest of my homework on my own (hopefully). Thank you!
Answer by jpg7n16(66) (Show Source): You can put this solution on YOUR website!
Well, there may not be a simple formula - but you can solve using 2 simple formulas. Plural. The easiest way to solve is to "stack" and reduce the two formulas. Here's what I mean:
Reggie invested part of his $30,000 in municipal bonds (let's call them "M") and the rest in corporate bonds (let's call them "C"). As a formula:
1)
Part 2: Each dollar of muni bonds (M) earns 6.5% (0.065), and each dollar of corporate bonds (C) earns 8.5% (0.085). Combined earnings gets you $2,190. As a formula:
2)
Now we can "stack" our 2 formulas, to solve for 1 variable.
1)
2)
Then, although it's not very fun, you need to make each formula have either the same number of M's OR C's. Since I like whole numbers, let's get rid of the crazy decimals by multiplying #2 by 1000.
1)
2)
Much better. Now we need the same number of one variable in each, so we'll be multiplying #1 by either 65 or 85. I'd recommend using the larger number to multiply - in this case 85.
1)
2)
Now both equations have 85 C's. Next, just subtract #2 from #1. You're left with

Therefore, Reggie invested $18,000 in muni bonds. Now we can solve for the amount in corporate bonds. Just plug 18,000 into the easier of the original 2 equations. Both will get the same answer, but #1 is easier by far! (Always choose the easier equation)
1)

And there you have it. Muni bonds: $18,000 and Corporate bonds: $12,000. You can calculate the interest if you need a check figure.

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