Question 1207734
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The solution in the link provided by the other tutor shows the standard method for solving a problem like this.<br>
If a formal algebraic solution is not required, here is a solution that uses a method that can be used to solve ANY 2-part "mixture" problem like this.<br>
(1) Betsy wants a $6000 return on her investment of $50,000.  Do some mental arithmetic to see that the required interest rate is 12%.<br>
(2) Compare the three interest rates 7%, 12%, and 15% (on a number line, if it helps) and observe/calculate that 12% is 5/8 of the way from 7% to 15%.<br>
(3) That means 5/8 of the $50,000 must be invested at the higher rate.<br>
5/8 of $50,000 = 5 * $6250 = $31,250<br>
ANSWER: $31,250 at 15%, the other $18,750 at 7%.<br>
CHECK: .15($31250)+.07($18750)=$4687.50+$1312.50=$6000<br>