SOLUTION: $9500 is invested, part of it at 10% and part of it at 8%. For a certain year, the total yield is $878.00. How much was invested at each rate? How much was invested at 10%?

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Question 373434: $9500 is invested, part of it at 10% and part of it at 8%. For a certain year, the total yield is $878.00. How much was invested at each rate?
How much was invested at 10%?
How much was invested at 8%?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = amount invested at 10%
Let b = amount invested at 8%
given:
(1) a+%2B+b+=+9500
.1a+%2B+.08b+=+878
(2) 10a+%2B+8b+=+87800
Multiply both sides of (1) by 8
and subtract (1) from (2)
(2) 10a+%2B+8b+=+87800
(1) -8a+-+8b+=+-76000
2a+=+11800
a+=+5900
and, since
(1) 5900+%2B+b+=+9500
b+=+3600
$5,900 was invested at 10% and $3,600 was invested at 8%
check answer:
.1a+%2B+.08b+=+878
.1%2A5900+%2B+.08%2A3600+=+878
590+%2B+288+=+878
878+=+878
OK