Question 68873
What is asked in the problem?
How much was invested in each bond?
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Given :
$5000 was invested in 2 different bonds
one yields 5% in one year
the other yielded 6% in one year
The total yield was $280.00
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Representation:
A = investment which yield 5% in dollars
B = investment which yield 6% in dollars
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Write an Equation. Translate the given sentences to mathematical sentence.
A + B = $5000
0.05A + 0.06B = $280.00 <-- it is better if you multiply 100 each term so that you will not deal with decimal later on.
0.05A + 0.06B = $280.00  is the same as 5A + 6B = 28000
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We can now use Substitution method to solve for the variable of the two equations.
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Here are the Steps using Substition method
1. In either equation, solve for one variable in terms of the other.
A + B = $5000
A = -B + 5000
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2. Substitute for that variable in the other equation. Solve.
5A + 6B = 28000
5(-B+5000) + 6B = 28000
-5B - 25000 + 6B = 28000
B = $ 3000 <<<<<<<< investment which yield 6% in dollars
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3. Substitute the result from step 2 in either equation. Solve for the other variable.
A + B = $5000, B = $3000
A + 3000 = 5000
A = $ 2000 <<<<<< investment which yield 5% in dollars
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4. Check the solution in both original equations.
A + B = $5000, A = $2000, B = $3000
2000 + 3000 = 5000
5000 = 5000 --------->> True
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5A + 6B = 28000, A = $2000, B = $3000
5(2000) + 6(3000) = 28000
10000 + 18000 = 28000
28000 = 28000 ----------->> True

<br> Therefore $2,000 was invested at 5% and $3,000 was invested at 6%