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A variety pack of chocolates contains chocolate candies with different fillings. one eighth of the candy has coconut filling, 5/16 of the chocolates have peanut butter filling,5/32 of the chocolates have orange cream filling. the rest of the candy is filled with chocolate cream. there are 8 candies with coconut filling. How many candies have chocolate cream filling?, what percent of the candy has peanut butter filling?,what fraction of the candy is orange or chocolate cream?

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Respuesta :

Answer : the number of candies having chocolate cream filling [tex]=26[/tex]

Percent of candy has peanut butter filling = 31.25%

Fraction of candy is orange or chocolate cream = [tex]\frac{9}{16}[/tex]

Explanation:

Part of candy has coconut filling =[tex]\frac{1}{8}[/tex]

Part of candy has peanut butter filling = [tex]\frac{5}{16}[/tex]

Part of candy has orange cream filling = [tex]\frac{5}{32}[/tex]

Remaining will be chocolate cream filling

= [tex]1-\frac{1}{8}-\frac{5}{16}-\frac{5}{32}\\=1-\frac{4+10+5}{32}\\=1-\frac{19}{32}\\=\frac{32-19}{32}\\=\frac{13}{32}[/tex]

Now, we have number of candies with coconut filling =8

so, [tex]\frac{1}{8}\times x=8[/tex] , where x is the total number of candies ,

x = 8×8=64

So, the number of candies having chocolate cream filling=

[tex]\frac{13}{32}\times 64\\=26[/tex]

Percent of candy has peanut butter filling = [tex]\frac{5}{16}\times 100\\=\frac{125}{4}[/tex]

∴Percent of candy has peanut butter filling = 31.25%

Fraction of candy is orange or chocolate cream

 [tex]=\frac{5}{32}+\frac{13}{32}\\=\frac{18}{32}\\=\frac{9}{16}[/tex]

∴Fraction of candy is orange or chocolate cream = [tex]\frac{9}{16}[/tex]