SOLUTION: Sang invested some money at 14% interest. Sang also invested $65 more than 4 times that amount at 7%. How much is invested at each rate if Sang receives $771.89 in interest after o

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Question 911496: Sang invested some money at 14% interest. Sang also invested $65 more than 4 times that amount at 7%. How much is invested at each rate if Sang receives $771.89 in interest after one year? (Round to two decimal places if necessary.)
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Total yearly interest for the two accounts is: $771.89
x=4y+65
0.07*x+0.14*y=771.89
Substitute for x
0.07*(4y+65)+0.14*y=771.89
Multiply out
0.28y+4.55+0.14*y=771.89
Combine like terms.
0.28y+4.55+0.14*y=771.89
0.28y+0.14*y=771.89-4.55
0.42*y=767.34
Isolate y
0.42*y=767.34
y=767.34/0.42
y=$1827.0 at 14%
y rounded off
y=$ 1827.00 at 14%
x=4y+65
x=4*1827.0+65
x=7308.0+65
x=$7373.0 at 7%
x rounded off
x=$ 7373.00 at 7%
y=$ 1827.00 at 7%
x=$ 7373.00 at 14%
Check
0.07*7373.0+0.14*1827.0=771.89
516.11+255.78=771.89
771.89=771.89
If this statement is TRUE and neither x nor y is negative then all is well
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