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there's the problem, can you PLEASE break it down so I can understand it??

Paul invests $15,250 in two different accounts. One pays an interest rate of 8.5% while the other account pays 10%. If he gains a total of $1411.75 annually, how much did he invest in each account?

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John M. | Analytical assistance -- Writing, Math, and moreAnalytical assistance -- Writing, Math, ...
4.8 4.8 (154 lesson ratings) (154)
Sarah, your question is about "translating" English into algebra symbols.  There are simpler ways to "solve" this problem, but I want to break it down as far as possible, because that is what I think is giving you trouble.  Let's take each sentence, and start labeling things as we go along.
"Paul invests $15,250 in two different accounts."
We're told there are 2 accounts, lets give them names "a" and "b".  We also know that Paul invested a total of $15,250 in these accounts, and when we total things, that is adding, so using the labels for the accounts, a & b, we translate this into "a + b = $15,250"
"One [account] pays an interest rate of 8.5% while the other account pays 10%"
This sentence gives us the interest rates on the two accounts.  This looks like a simple interest problem.  The generic formula for simple interest is that the Interest equals Principal times Rate times Time (I = Prt). Let's create two equations, one for each account.  Label these interest rates "r", and the rate on account a as r(a) = 8.5% and the rate on account b as r(b) = 10%; a and b are the Principal amounts in each account, I(a) as the interest paid on account a and I(b) the interest on account b, and use t for time in both equations.  Feel free to use any labels you want, but I created something like this:
I(a) = a • r(a) • t
I(b) = b • r(b) • t
"If he gains a total of $1,411.75 annually, how much did he invest in each account?"
The total gain from an investment is the interest, so Paul's total gain is the interest he receives from account a and the interest he gets from account b, and as a total, we are adding again, so we translate the first clause as I(a) + I(b) = $1,411.75. 
We also know that since we are given an annual amount of interest, that the time "t" is 1 year, i.e. t = 1.
So let's sum up.  We know
a + b = $15,250
I(a) = a • r(a) • t
I(b) = b • r(b) • t
I(a) + I(b) = $1,411.75
r(a) = 8.5%
r(b) = 10%
t = 1
We have labelled 7 variables [a, b, I(a), r(a), t, I(b), & r(b)] and have seven equations, so it is solvable.  But I would recommend keeping a + b = $15,250, and plugging all the rest of the information into
I(a) + I(b) = $1,411.75
Plugging in for I(a) and I(b)
[a • r(a) • t] + [b • r(b) • t] = $1,411.75
When working with interest rates expressed as percentages, remember that you need to use the decimal form for the math to workout, so 8.5% is equal to 0.085 and 10% is equal to 0.1, so let's plug in r(a), r(b) and t into that equation
[a • 0.085 • 1] + [b • 0.1 • 1] = $1,411.75
Simplifying that equation produces
0.085 • a + 0.1 • b = $1,411.75
And returning to our first equation
a + b = $15,250
These are two fairly straightforward equations, with two unknowns (a & b), and they are the unknowns the question asks for (how much did he invest in each account).
I'll leave the equation for you to solve; you can use substitution or any other method you prefer.  Feel free to ask a follow-up question or email me, and I'd be happy to walk you through solving two equation--two unknown problems in more detail.  I hope this helps.  John
Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
5.0 5.0 (9 lesson ratings) (9)
x=amount invested in one account
y=amount invested in a second account
solve for x in x+y=15,250
substitute into the equation 0.085x+0.1y=1411.75
$7550 invested at 8.5 %
$7700 invested at 10 %
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
 I break it down for you . Always choose a variable for unknown ( what problem is asking you to find out)
 X - amount invested in 8.5%
15250 - X = amount invested in 10%
  Gain in 8.5%= x (0.085)
  Gain in 10% account = ( 15250 - X ) 0.10
    X ( 0.085) + ( 15200 - X ) =1411.75       Total gain in 2 accounts
   Now by converting English statement of problem to algebraic expression , came up with a equation of 
  one unknown to solve, and I let you to solve.
Andre W. | Friendly tutor for ALL math and physics coursesFriendly tutor for ALL math and physics ...
5.0 5.0 (3 lesson ratings) (3)
Let x and y be the amounts invested in the two accounts. Then
The total interest is
0.085*x + 0.1*y=1411.75
Solve the first equation for y and substitute into the second equation:
0.085*x + 0.1*(15250-x)=1411.75
Solve for x. After a little bit of algebra :) , you get
x=7550,  y=7700