SOLUTION: select the set of equations that represent the following situation. Mary invested one amount at 10% simple interest, and a second amount at 3% interest, earning $21.72 in one year.

Algebra ->  Linear-equations -> SOLUTION: select the set of equations that represent the following situation. Mary invested one amount at 10% simple interest, and a second amount at 3% interest, earning $21.72 in one year.      Log On


   



Question 624391: select the set of equations that represent the following situation. Mary invested one amount at 10% simple interest, and a second amount at 3% interest, earning $21.72 in one year. If she had switched the amounts, she would have earned $15.07. What were the two amounts.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+.1a+%2B+.03b+=+21.72+
+.1b+%2B+.03a+=+15.07+
-------------------
(1) +10a+%2B+3b+=+2172+
(2) +10b+%2B+3a+=+1507+
Multiply both sides of (1) by +3+
and both sides of (2) by +10+
(1) +30a+%2B+9b+=+6516+
(2) +30a+%2B+100b+=+15070+
Subtract (1) from (2)
(2) +30a+%2B+100b+=+15070+
(1) +-30a+-+9b+=+-6516+
+91b+=+8554+
+b+=+94+
Plug this result back into either equation
(2) +10%2A94+%2B+3a+=+1507+
(2) +940+%2B+3a+=+1507+
(2) +3a+=+1507+-+940+
(2) +3a+=+567+
(2) +a+=+189+
$189 was invested @ 10%
$94 was invested @ 3%
check:
+.1b+%2B+.03a+=+15.07+
+.1%2A94+%2B+.03%2A189+=+15.07+
+9.4+%2B+5.67+=+15.07+
+15.07+=+15.07+
OK