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1. George has $700 to invest. Suppose he invests $300 at 6% interest. At what rate must he invest the other $400 so that the two investments yield more than $70 of yearly interest?
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\n" ); document.write( "6% interest rate:
\n" ); document.write( "Principal = 300
\n" ); document.write( "Rate = 0.06
\n" ); document.write( "Interest = 300 * 0.06 = 18
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\n" ); document.write( "Other interest rate:
\n" ); document.write( "Principal = 400
\n" ); document.write( "Rate = 52/400 = 0.13
\n" ); document.write( "Interest = 70 - 18 = 52
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\n" ); document.write( "To yield MORE than $70 worth of interest, the $400 must be invested at a rate HIGHER than 13%.
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\n" ); document.write( "2. Angie bought some golf balls for $5. If each ball had cost $0.25 less, she could have purchased one more ball for the same amount of money. How many balls did Angie buy?
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\n" ); document.write( "c = cost of each ball
\n" ); document.write( "n = number of balls
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\n" ); document.write( "c * n = 5
\n" ); document.write( "(c - 0.25) * (n + 1) = 5
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\n" ); document.write( "This means:
\n" ); document.write( "c * n = (c - 0.25) * (n + 1)
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\n" ); document.write( "Simplify:
\n" ); document.write( "cn = cn - 0.25n + c - 0.25
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\n" ); document.write( "Solve for c:
\n" ); document.write( "0 = c - 0.25n - 0.25
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\n" ); document.write( "c = 0.25n + 0.25
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\n" ); document.write( "From earlier, we know:
\n" ); document.write( "c * n = 5
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\n" ); document.write( "Substitute 0.25n + 0.25 for c:
\n" ); document.write( "c * n = 5
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\n" ); document.write( "(0.25n + 0.25) * n = 5
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\n" ); document.write( "Solve for n:
\n" ); document.write( "0.25n² + 0.25n = 5
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\n" ); document.write( "0.25n² + 0.25n - 5 = 0
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\n" ); document.write( "Use quadratic formula.
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\n" ); document.write( "You will find that n = 4 and n = -5. Since the number of balls purchased cannot be a negative number, you can throw out n = -5. We are left with n = 4.
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\n" ); document.write( "We now know Angie bought 4 balls.
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\n" ); document.write( "From earlier:
\n" ); document.write( "c * n = 5
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\n" ); document.write( "Substitute '4' for n:
\n" ); document.write( "c * 4 = 5
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\n" ); document.write( "Solving for c, we find that c = 1.25.
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\n" ); document.write( "In summary, Angie bought four balls at $1.25 apiece. (Had each ball been $0.25 cheaper, she could've bought five balls at $1.00 apiece.)