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Jeff bought a box of bundt cakes containing a total of 288 pieces of chocolate bundt cakes and vanilla bundt cakes. 4/9 of the bundt cakes were chocolate and the rest were vanilla. After he ate some chocolate bundt cakes, the number of chocolates left was 5/8 of the total number of chocolates at first. How many chocolate cakes did he eat?

 Oct 17, 2021
 #1
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How many chocolate cakes did he eat?

 

Hello Guest!

 

\(\frac{5}{8}\cdot \frac{4}{9}\cdot 288+\frac{5}{9}\cdot 288=288-x\\ x=288-(\frac{5}{8}\cdot \frac{4}{9}\cdot 288+\frac{5}{9}\cdot 288)\) 

\(x=48\)

 

48 chocolate cakes did Jeff eat.

laugh  !

 Oct 24, 2021
 #2
avatar+294 
+1

Let x be the number of chocolate cakes bought by Jeff

The total number of cakes including chocolate cakes and vanilla cakes is 288.

∴ Number of vanilla cakes = 288 - x.

Out of total cakes 4/9 are chocolate & the rest were vanilla.

∴ Number of chocolate cakes is

            x = 4/9 x (total number of cakes)

               = 4/9 * 288 = 1152/9 = 128

∴ Number of vanilla cakes = 288 - 128 = 160

∴ Jeff bought 128 chocolate cakes & 160 vanilla cakes

Jeff ate some chocolate cakes, the number of chocolates left was 5/8 of the total number of chocolate at first

Let y be the number of chocolate left.

∴ y = 5/8 x (total number of chocolate at first)

      = 5/8 * 128 = 640/8 = 80

 

∴ (chocolate cake ate by Jeff) + y = Total number of chocolate cakes

 

    ∴ (Chocolate cake ate by Jeff) + 80 = 128

      => Choclate cake ate by Jeff = 128 - 80 = 48.

∴ Jeff eat 48 chocolate cakes.

 Oct 24, 2021

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