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Sally had some chocolate chips. She used 1/3 of the chocolate chips to decorate 12 small Christmas cakes. She also used 3/4 of the remaining chocolate chips to decorate 10 big Christmas cakes. Given that each Christmas cake had 16 more chocolate chips than each small Christmas tree, how many chocolate chips did Sally have at first?

 Nov 5, 2021
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Define Variables:

C = Total Chocolate Chips

S = Small Christmas Cake/Tree

B = Big Christmas Cake

 

Set the 3 Equations:

  1. 1/3 C = 12 S

  2. 3/4 (2/3 C) = 10 B

  3. B = 16 + S

Begin Solving for Variables:

  • 1/2 C = 10 (16 + S)

  • 1/2 C = 160 + 10S

  • C = 320 + 20S

 

  • 1/3 (320 + 20S) = 12 S

  • 320 + 20S = 36S

  • S = 20

Solve for Rest of Variables:

  • B = 16 + (20) = 36

  • C = 320 + 20 x (20) = 720

 

Check:

  • 1/3 (720) = 240 | 12 (20) = 240
  • 3/4 (2/3 (720) = 360 | 10 (36) = 360
  • (36) = 16 + (20) = 36
 Nov 6, 2021

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