SOLUTION: A man has two investments, one paying 5% annual interest and the other at 8%. The total annual income from the two investments is P 4,650. If the interest rates were interchanged,

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A man has two investments, one paying 5% annual interest and the other at 8%. The total annual income from the two investments is P 4,650. If the interest rates were interchanged,       Log On


   

Question 1066863: A man has two investments, one paying 5% annual interest and the other at 8%. The total annual income from the two investments is P 4,650. If the interest rates were interchanged, the total annual income would be P 5,100. Find the amount invested. of each rate.
Found 2 solutions by josmiceli, Boreal:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+I%5B1%5D+=+P%5B1%5D%2Ar%5B1%5D%2At+
(1) +I%5B1%5D+=+P%5B1%5D%2A.05%2A1+
-----------------------
+I%5B2%5D+=+P%5B2%5D%2Ar%5B2%5D%2At+
(2) +I%5B2%5D+=+P%5B2%5D%2A.08%2A1+
-----------------------
(3) +I%5B1%5D+%2B+I%5B2%5D+=+4650+
-----------------------
Now just swap the interest rates
+I%5B1%5D+=+P%5B1%5D%2Ar%5B2%5D%2At+
(4) +I%5B3%5D+=+P%5B1%5D%2A.08%2A1+
-----------------------
+I%5B2%5D+=+P%5B2%5D%2Ar%5B1%5D%2At+
(5) +I%5B4%5D+=+P%5B2%5D%2A.05%2A1+
-----------------------
(6) +I%5B3%5D+%2B+I%5B4%5D+=+5100+
========================
(3) +I%5B1%5D+%2B+I%5B2%5D+=+4650+
Use (1) and (2) to get:
(3) +.05P%5B1%5D+%2B+.08P%5B2%5D+=+4650+
---------------------------------
(6) +I%5B3%5D+%2B+I%5B4%5D+=+5100+
Use (4) and (5) to get:
(6) +.08P%5B1%5D+%2B+.05P%5B2%5D+=+5100+
---------------------------------
(3) +5P%5B1%5D+%2B+8P%5B2%5D+=+465000+
(6) +8P%5B1%5D+%2B+5P%5B2%5D+=+510000+
Multiply both sides of (3) by +8+
Multiply both sides of (6) by +5+
Subtract (6) from (3)
---------------------------------
(3) +40P%5B1%5D+%2B+64P%5B2%5D+=+3720000+
(6) +-40P%5B1%5D+-+25P%5B2%5D+=+-2550000+
------------------------------------
+39P%5B2%5D+=+1170000+
+P%5B2%5D+=+30000+
and
(3) +5P%5B1%5D+%2B+8P%5B2%5D+=+465000+
(3) +5P%5B1%5D+%2B+8%2A30000+=+465000+
(3) +5P%5B1%5D+=+465000+-+240000+
(3) +5P%5B1%5D+=+225000+
(3) +P%5B1%5D+=+45000+
---------------------------------
P 45,000 is invested @ 5%
P 30,000 is invested @ 8%
--------------------------
check:
(1) +I%5B1%5D+=+P%5B1%5D%2A.05%2A1+
(1) +I%5B1%5D+=+45000%2A.05%2A1+
(1) +I%5B1%5D+=+2250+
and
(2) +I%5B2%5D+=+P%5B2%5D%2A.08%2A1+
(2) +I%5B2%5D+=+30000%2A.08%2A1+
(2) +I%5B2%5D+=+2400+
and
(3) +I%5B1%5D+%2B+I%5B2%5D+=+4650+
(3) +2250+%2B+2400+=+4650+
(3) +4650+=+4650+
OK
You can check +I%5B3%5D+ and +I%5B4%5D+
the same way



Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x and y are the two amounts.
.05x+.08y=4650
.08x+.05y=5100
5x+8y=465000, multiplying by 100
8x+5y=510000
Multiply the top by -8 and the bottom by +5 to eliminate x
-40x-64y=-3720000
40x+25y=2550000
-39y=-1170000
y=P30000
5x+240000=465000
5x=225000
x=P45000
.05(45000)+.08(30000)=2250+2400=4650
.08(45000)+.05(30000)=3600+1500=5100