SOLUTION: helen has 1/5 of her portfolio in U.S. stocks, 1/8 of her portfolio in European stocks, and 1/10 of her portfolio in Japanese stocks. The remainder is invested in municipal bonds.

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: helen has 1/5 of her portfolio in U.S. stocks, 1/8 of her portfolio in European stocks, and 1/10 of her portfolio in Japanese stocks. The remainder is invested in municipal bonds.       Log On


   

Question 177306: helen has 1/5 of her portfolio in U.S. stocks, 1/8 of her portfolio in European stocks, and 1/10 of her portfolio in Japanese stocks. The remainder is invested in municipal bonds. What fraction of her portfolio is invested in municipal bonds? What percent is invested in municipal bonds?
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Answer by gonzo(654) About Me  (Show Source):
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1%2F5+%2B+1%2F8+%2B+1%2F10+%2B+x+=+1
multiply both sides of this equation by 40 to get:
40%2F5+%2B+40%2F8+%2B+40%2F10+%2B+40x+=+40
simplify to get:
8+%2B+5+%2B+4+%2B+40x+=+40
combine like terms to get:
17+%2B+40x+=+40
subtract 17 from both sides to get:
+40x+=+23
divide both sides by 40 to get:
x+=+23%2F40
23%2F40+%2A+100+=+57.5
23/40 is the same as 57.5%
to prove this is correct, plug it into the original equation.
since the sum of all the parts equals the whole, then the sum of all the fractions must = 1.
1/5 + 1/8 + 1/10 + 23/40 = 1
1/5 = 8/40
1/8 = 5/40
1/10 = 4/40
add these together to get:
8/40 + 5/40 + 4/40 + 23/40 = (8+5+4+23)/40 = 40/40 = 1
your answer is:
the fraction of her portfolio invested in municipal bonds is 23/40
the percent of her portfolio invested in municipal bonds is 57.5%