Question 182696
ok you have the right idea...many times when they throw something new into a problem it throws us off just a little. We know that we have two unknowns. The amounts invested at 6 and 10%. So we know we have to come up with 2 equations to solve.....lets, as you say, call the amount invested at 6%, x and the amount invested at 10% lets call y. Here is what we know without much thinking
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x+y=15000...............eq 1
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so we have one equation under our belt.
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now typically in this type of problem we would have another equation of the form
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.06x+.1y=(profit). But they through a twist in this one. We know the profit of one in terms of the other...... we know the profit for the 6% is .06x and we know the profit for 10% is .1y. But we also know that the profit from the 10% is 1000 more than the profit from the 6%, so lets write it out
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.06x=.1y+1000..........eq 2
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now we have  2 equations
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x+y=15000...............eq 1
.1y=.06x+1000..........eq 2
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rewrite eq 1 to {{{highlight(x)=red(15000-y)}}} and plug that value into eq 2
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.1y=.06(15000-y)+1000
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.1y=900-.06y+1000
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.16y=1900
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${{{highlight(y=11875)}}}amount invested at 10%
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${{{highlight(x)=red(15000-y)=15000-11875=highlight(3125)}}}amount invested at 6%
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