SOLUTION: I've been working on profit equations and am starting to understand, but this one added something new and I don't know how to deal with it. Question

SOLUTION: I've been working on profit equations and am starting to understand, but this one added something new and I don't know how to deal with it. Question - Rose invested some of her $1

Question 182696This question is from textbook Teaching Textbooks
: I've been working on profit equations and am starting to understand, but this one added something new and I don't know how to deal with it.
Question - Rose invested some of her $15,000 in bonds that made a 6% profit and the rest in bonds that made a 10% profit. If the profit on the 10% bonds was $1,000 more than the profit on the 6% bonds, how much did she invest in the 6% bonds?
I think that if x= amount invested on the 6% bonds then
.06x = .10(15,000 -x), but I don't know where to put the extra $1000 profit? Does it even belong in the equation?
I tried .06x = .10+1,000(15,000-x), but that is a mess. Thanks for your help! This question is from textbook Teaching Textbooks

Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
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
:
x+y=15000...............eq 1
:
so we have one equation under our belt.
:
now typically in this type of problem we would have another equation of the form
:
.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
:
.06x=.1y+1000..........eq 2
:
now we have 2 equations
:
x+y=15000...............eq 1
.1y=.06x+1000..........eq 2
:
rewrite eq 1 to and plug that value into eq 2
:
.1y=.06(15000-y)+1000
:
.1y=900-.06y+1000
:
.16y=1900
:
$amount invested at 10%
:
$amount invested at 6%
:

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