SOLUTION: A stockbroker has money in three accounts. The interest rates on the three accounts are 8%,9%, and 10%. If she has twice as much money invested at 9% as she does in 8%, three times

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Question 1060552: A stockbroker has money in three accounts. The interest rates on the three accounts are 8%,9%, and 10%. If she has twice as much money invested at 9% as she does in 8%, three times as much at 10% as she has at 8%, and the total interest for the year is $112, how much is invested at each rate?

JoAnn works in a publicity office at the state university. She is paid $11.50 an hour for the first 35 hours she works each week and $17.25 an hour for every hour after that. If she makes $471.50 one week, how many hours did she work?

The difference of x and 12 is 13.
Please help me. Im so confused :(

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
For simple interest, and also
for 1 year:
+I+=+P%2Ar%2At+
where +P+ is the amount invested
at rate +r+
---------------------
+I%5B1%5D+=+P%2A.08%2A1+
+I%5B2%5D+=+2P%2A.09%2A1+
+I%5B3%5D+=+3P%2A.1%2A1+
---------------------
+I%5B1%5D+%2B+I%5B2%5D+%2B+I%5B3%5D+=+112+
+.08P+%2B+.18P+%2B+.3P+=+112+
+.56P+=+112+
+P+=+200+
+2P+=+400+
+3P+=+600+
----------------
$200 is invested at 8%
$400 is invested at 9%
$600 is invested at 10%
-------------------------
-------------------------
Let +t+ = the number of hours she worked
for the week
+471.5+=+11.5%2A35+%2B+17.25%2A%28+t+-+35+%29+
+471.5+=+402.5+%2B+17.25t+-+603.75+
+17.25t+=+471.5+%2B+603.75+-+402.5+
+17.25t+=+69+%2B+603.75+
+17.25t+=+672.75+
+t+=+39+
She worked 39 hrs for the week
------------------------------
check:
+471.5+=+11.5%2A35+%2B+17.25%2A%28+t+-+35+%29+
+471.5+=+11.5%2A35+%2B+17.25%2A%28+39+-+35+%29+
+471.5+=+402.5+%2B+69+
+471.5+=+471.5+
OK