SOLUTION: Jenny has R90 000 to invest. She has chosen one relatively safe investment fund that has an annual yield of 10% and another, riskier one that has a 15% annual yield. How much shou

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: Jenny has R90 000 to invest. She has chosen one relatively safe investment fund that has an annual yield of 10% and another, riskier one that has a 15% annual yield. How much shou      Log On

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Question 1091495: Jenny has R90 000 to invest. She has chosen one relatively safe investment fund that has an annual yield of
10% and another, riskier one that has a 15% annual yield. How much should she invest in each fund if she
would like to earn R10 000 in one year from her investments?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = amount to invest @ 10%
Let +b+ = amount to invest @ 15%
--------------------------------------
(1) +a+%2B+b+=+90000+
(2) +.1a+%2B+.15b+=+10000+
------------------------------
(2) +10a+%2B+15b+=+1000000+
(2) +2a+%2B+3b+=+200000+
Multiply both sides of (1) by +2+
and subtract (1) from (2)
(2) +2a+%2B+3b+=+200000+
(1) +-2a+-2b+=+-180000+
----------------------------
+b+=+20000+
and
(1) +a+%2B+b+=+90000+
(1) +a+%2B+20000+=+90000+
(1) +a+=+70000+
----------------------------
She should invest R70 000 @ 10% and
R20 000 @ 15%
--------------------
check:
(2) +.1a+%2B+.15b+=+10000+
(2) +.1%2A70000+%2B+.15%2A20000+=+10000+
(2) +7000+%2B+3000+=+10000+
OK